Quantifying the rheological and hemodynamic characteristics of sickle cell anemia

High-throughput quantification of red blood cell deformability and oxygen saturation to probe mechanisms of sickle cell disease

The complex, systemic pathology of sickle cell disease is driven by multiple mechanisms including red blood cells (RBCs) stiffened by polymerized fibers of deoxygenated sickle hemoglobin. A critical step toward understanding the pathologic role of polymer-containing RBCs is quantifying the biophysical changes in these cells in physiologically relevant oxygen environments. We have developed a microfluidic platform capable of simultaneously measuring single RBC deformability and oxygen saturation under controlled oxygen and shear stress. We found that RBCs with detectable amounts of polymer have decreased oxygen affinity and decreased deformability. Surprisingly, the deformability of the polymer-containing cells is oxygen-independent, while the fraction of these cells increases as oxygen decreases. We also find that some fraction of these cells is present at most physiologic oxygen tensions, suggesting a role for these cells in the systemic pathologies. Additionally, the ability to measure these pathological cells should provide clearer targets for evaluating therapies.

In silico modeling of patient-specific blood rheology in type 2 diabetes mellitus

Increased blood viscosity in type 2 diabetes mellitus (T2DM) is a risk factor for the development of insulin resistance and diabetes-related vascular complications; however, individuals with T2DM exhibit heterogeneous hemorheological properties, including cell deformation and aggregation. Using a multiscale red blood cell (RBC) model with key parameters derived from patient-specific data, we present a computational study of the rheological properties of blood from individual patients with T2DM. Specifically, one key model parameter, which determines the shear stiffness of the RBC membrane (μ) is informed by the high-shear-rate blood viscosity of patients with T2DM. At the same time, the other, which contributes to the strength of the RBC aggregation interaction (D0), is derived from the low-shear-rate blood viscosity of patients with T2DM. The T2DM RBC suspensions are simulated at different shear rates, and the predicted blood viscosity is compared with clinical laboratory-measured data. The results show that the blood viscosity obtained from clinical laboratories and computational simulations are in agreement at both low and high shear rates. These quantitative simulation results demonstrate that the patient-specific model has truly learned the rheological behavior of T2DM blood by unifying the mechanical and aggregation factors of the RBCs, which provides an effective way to extract quantitative predictions of the rheological properties of the blood of individual patients with T2DM.

Cardiovascular consequences of sickle cell disease

Sickle cell disease (SCD) is an inherited blood disorder caused by a single point mutation within the beta globin gene. As a result of this mutation, hemoglobin polymerizes under low oxygen conditions causing red blood cells to deform, become more adhesive, and increase in rigidity, which affects blood flow dynamics. This process leads to enhanced red blood cell interactions with the endothelium and contributes to vaso-occlusion formation. Although traditionally defined as a red blood cell disorder, individuals with SCD are affected by numerous clinical consequences including stroke, painful crisis episodes, bone infarctions, and several organ-specific complications. Elevated cardiac output, endothelium activation along with the sickling process, and the vaso-occlusion events pose strains on the cardiovascular system. We will present a review of the cardiovascular consequences of sickle cell disease and show connections with the vasculopathy related to SCD. We will also highlight biophysical properties and engineering tools that have been used to characterize the disease. Finally, we will discuss therapies for SCD and potential implications on SCD cardiomyopathy.

Circulating cell clusters aggravate the hemorheological abnormalities in COVID-19

Microthrombi and circulating cell clusters (CCCs) are common microscopic findings in patients with COVID-19 at different stages in the disease course, implying that they may function as the primary drivers in disease progression. Inspired by a recent flow imaging cytometry study of the blood samples from patients with COVID-19, we perform computational simulations to investigate the dynamics of different types of CCCs, namely white blood cell (WBC) clusters, platelet clusters and red blood cell (RBC) clusters, over a range of shear flows and quantify their impact on the viscosity of the blood. Our simulation results indicate that the increased level of fibrinogen in patients with COVID-19 can promote the formation of RBC clusters at relatively low shear rates, thereby elevating the blood viscosity, a mechanism that also leads to an increase in viscosity in other blood diseases, such as sickle cell disease and type 2 diabetes mellitus. We further discover that the presence of WBC clusters could also aggravate the abnormalities of local blood rheology. In particular, the extent of elevation of the local blood viscosity is enlarged as the size of the WBC clusters grows. On the other hand, the impact of platelet clusters on the local rheology is found to be negligible, which is likely due to the smaller size of the platelets. The difference in the impact of WBC and platelet clusters on local hemorheology provides a compelling explanation for the clinical finding that the number of WBC clusters is significantly correlated with thrombotic events in COVID-19 whereas platelet clusters do not. Overall, our study demonstrates that our computational models based on dissipative particle dynamics can serve as a powerful tool to conduct quantitative investigation of the mechanism causing the pathological alterations of hemorheology and explore their connections to the clinical manifestations in COVID-19.

Computational Characterization of Mechanical, Hemodynamic, and Surface Interaction Conditions: Role of Protein Adsorption on the Regenerative Response of TEVGs

Currently available small diameter vascular grafts (<6 mm) present several long-term limitations, which has prevented their full clinical implementation. Computational modeling and simulation emerge as tools to study and optimize the rational design of small diameter tissue engineered vascular grafts (TEVG). This study aims to model the correlation between mechanical-hemodynamic-biochemical variables on protein adsorption over TEVG and their regenerative potential. To understand mechanical-hemodynamic variables, two-way Fluid-Structure Interaction (FSI) computational models of novel TEVGs were developed in ANSYS Fluent 2019R3^® and ANSYS Transient Structural^® software. Experimental pulsatile pressure was included as an UDF into the models. TEVG mechanical properties were obtained from tensile strength tests, under the ISO7198:2016, for novel TEVGs. Subsequently, a kinetic model, linked to previously obtained velocity profiles, of the protein-surface interaction between albumin and fibrinogen, and the intima layer of the TEVGs, was implemented in COMSOL Multiphysics 5.3^®. TEVG wall properties appear critical to understand flow and protein adsorption under hemodynamic stimuli. In addition, the kinetic model under flow conditions revealed that size and concentration are the main parameters to trigger protein adsorption on TEVGs. The computational models provide a robust platform to study multiparametrically the performance of TEVGs in terms of protein adsorption and their regenerative potential.

The effect of rigid cells on blood viscosity: linking rheology and sickle cell anemia

Sickle cell anemia (SCA) is a disease that affects red blood cells (RBCs). Healthy RBCs are highly deformable objects that under flow can penetrate blood capillaries smaller than their typical size. In SCA there is an impaired deformability of some cells, which are much stiffer and with a different shape than healthy cells, and thereby affect regular blood flow. It is known that blood from patients with SCA has a higher viscosity than normal blood. However, it is unclear how the rigidity of cells is related to the viscosity of blood, in part because SCA patients are often treated with transfusions of variable amounts of normal RBCs and only a fraction of cells will be stiff. Here, we report systematic experimental measurements of the viscosity of a suspension varying the fraction of rigid particles within a suspension of healthy cells. We also perform systematic numerical simulations of a similar mixed suspension of soft RBCs, rigid particles, and their hydrodynamic interactions. Our results show that there is a rheological signature within blood viscosity to clearly identify the fraction of rigidified cells among healthy deformable cells down to a 5% volume fraction of rigidified cells. Although aggregation of RBCs is known to affect blood rheology at low shear rates, and our simulations mimic this effect via an adhesion potential, we show that such adhesion, or aggregation, is unlikely to provide a physical rationalization for the viscosity increase observed in the experiments at moderate shear rates due to rigidified cells. Through numerical simulations, we also highlight that most of the viscosity increase of the suspension is due to the rigidity of the particles rather than their sickled or spherical shape. Our results are relevant to better characterize SCA, provide useful insights relevant to rheological consequences of blood transfusions, and, more generally, extend to the rheology of mixed suspensions having particles with different rigidities, as well as offering possibilities for developments in the field of soft material composites.

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.

In silico biophysics and hemorheology of blood hyperviscosity syndrome

Hyperviscosity syndrome (HVS) is characterized by an increase of the blood viscosity by up to seven times the normal blood viscosity, resulting in disturbances to the circulation in the vasculature system. HVS is commonly associated with an increase of large plasma proteins and abnormalities in the properties of red blood cells, such as cell interactions, cell stiffness, and increased hematocrit. Here, we perform a systematic study of the effect of each biophysical factor on the viscosity of blood by employing the dissipative particle dynamic method. Our in silico platform enables manipulation of each parameter in isolation, providing a unique scheme to quantify and accurately investigate the role of each factor in increasing the blood viscosity. To study the effect of these four factors independently, each factor was elevated more than its values for a healthy blood while the other factors remained constant, and viscosity measurement was performed for different hematocrits and flow rates. Although all four factors were found to increase the overall blood viscosity, these increases were highly dependent on the hematocrit and the flow rates imposed. The effect of cell aggregation and cell concentration on blood viscosity were predominantly observed at low shear rates, in contrast to the more magnified role of cell rigidity and plasma viscosity at high shear rates. Additionally, cell-related factors increase the whole blood viscosity at high hematocrits compared with the relative role of plasma-related factors at lower hematocrits. Our results, mapped onto the flow rates and hematocrits along the circulatory system, provide a correlation to underpinning mechanisms for HVS findings in different blood vessels.

A microfluidic computational fluid dynamics model for cellular interaction studies of sickle cell disease vaso-occlusions

Individuals with sickle cell disease are plagued with vaso-occlusions, chronic blockages within the vasculature. Several factors including stiffer sickle red blood cells and increased cell aggregation contribute to vaso-occlusion formation; however much remains to be understood. We present a computational fluid dynamics blood flow simulation within a microfluidic platform using the Carreau model and Murray's law. Vaso-occlusions form preferentially near bifurcations within 60 s in the sickle cell disease simulation. Velocity profiles and shear rates align with clinical and experimental reports. We assert that results from this study can be utilized to inform experimental investigations and microfluidic system design decisions.

Confined filaments in soft vesicles - the case of sickle red blood cells

Abnormal shapes of red blood cells (RBC) have been associated with various diseases. Diverse RBC shapes have also been intriguing for membrane biophysics. Here we focus on sickle shaped RBC which form due to abnormal growth of semi-rigid hemoglobin (HbS) fibers confined in RBC. Using the area difference elasticity (ADE) model for RBC and worm-like chain model for the confined HbS fibers, we explore shape deformations at equilibrium using Monte-Carlo simulations. We show that while a single HbS fiber is not rigid enough to produce sickle like deformation, a fiber bundle can do so. We also consider multiple disjoint filaments and find that confinement can generate multipolar RBC shapes and can even promote helical filament conformations which have not been discussed before. We show that the same model, when applied to microtubules confined in phospholipid vesicles, predicts vesicle tubulation. In addition we reproduce the tube collapse transition and tennis racket type vesicle shapes, as reported in experiments. We conclude that with a decrease in the surface area to volume ratio, and membrane rigidity, the vesicles prefer tubulation over sickling. The highlight of this work is several important non-axisymmetric RBC and vesicle shapes, which have never been explored in simulations.

Impact of A Six Week Training Program on Ventilatory Efficiency, Red Blood Cell Rheological Parameters and Red Blood Cell Nitric Oxide Signaling in Young Sickle Cell Anemia Patients: A Pilot Study

Patients with sickle cell anemia (SCA) show impaired ventilatory efficiency, altered blood rheology, high levels of oxidative/nitrosative stress and enhanced hemolysis with large amounts of circulating free hemoglobin, which reduces nitric oxide (NO) bioavailability. The aim of the study was to investigate whether physical exercise could improve these physiological and biological markers described to contribute to SCA pathophysiology. Twelve SCA patients participated in a controlled six weeks training program with moderate volume (two sessions per week with 15–30 min duration per session) and intensity (70% of the first ventilatory threshold). Parameters were compared before (T0) and after (T1) training. Daily activities were examined by a questionnaire at T0 and one year after the end of T1. Results revealed improved ventilatory efficiency, reduced nitrosative stress, reduced plasma free hemoglobin concentration, increased plasma nitrite levels and altered rheology at T1 while no effect was observed for exercise performance parameters or hematological profile. Red blood cell (RBC) NO parameters indicate increased NO bioavailability which did not affect RBC deformability. Participants increased their daily life activity level. The data from this pilot study concludes that even low intensity activities are feasible and could be beneficial for the health of SCA patients.

Quantifying Shear-Induced Deformation and Detachment of Individual Adherent Sickle Red Blood Cells

Vaso-occlusive crisis, a common painful complication of sickle cell disease, is a complex process triggered by intercellular adhesive interactions among blood cells and the endothelium in all human organs (e.g., the oxygen-rich lung as well as hypoxic systems such as liver and kidneys). We present a combined experimental-computational study to quantify the adhesive characteristics of sickle mature erythrocytes (SMEs) and irreversibly sickled cells (ISCs) under flow conditions mimicking those in postcapillary venules. We employed an in vitro microfluidic cell adherence assay, which is coated uniformly with fibronectin. We investigated the adhesion dynamics of SMEs and ISCs in pulsatile flow under well-controlled hypoxic conditions, inferring the cell adhesion strength by increasing the flow rate (or wall shear stress (WSS)) until the onset of cell detachment. In parallel, we performed simulations of individual SMEs and ISCs under shear. We introduced two metrics to quantify the adhesion process, the cell aspect ratio (AR) as a function of WSS and its rate of change (the dynamic deformability index). We found that the AR of SMEs decreases significantly with the increase of WSS, consistent between the experiments and simulations. In contrast, the AR of ISCs remains constant in time and independent of the flow rate. The critical WSS value for detaching a single SME in oxygenated state is in the range of 3.9-5.5 Pa depending on the number of adhesion sites; the critical WSS value for ISCs is lower than that of SMEs. Our simulations show that the critical WSS value for SMEs in deoxygenated state is above 6.2 Pa (multiple adhesion sites), which is greater than their oxygenated counterparts. We investigated the effect of cell shear modulus on the detachment process; we found that for the same cell adhesion spring constant, the higher shear modulus leads to an earlier cell detachment from the functionalized surface. These findings may aid in the understanding of individual roles of sickle cell types in sickle cell disease vaso-occlusion.

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.

Structural modelling of the cardiovascular system

Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.

Local Hematocrit Fluctuation Induced by Malaria-Infected Red Blood Cells and Its Effect on Microflow

We investigate numerically the microscale blood flow in which red blood cells (RBCs) are partially infected by Plasmodium falciparum, the malaria parasite. The infected RBCs are modeled as more rigid cells with less deformability than healthy ones. Our study illustrates that, in a 10 μm microvessel in low-hematocrit conditions (18% and 27%), the Plasmodium falciparum-infected red blood cells (Pf-IRBCs) and healthy ones first form a train of cells. Because of the slow moving of the Pf-IRBCs, the local hematocrit (H_ct) near the Pf-IRBCs is then increased, to approximately 40% or even higher values. This increase of the local hematocrit is temporary and is kept for a longer length of time because of the long RBC train formed in 27%-H_ct condition. Similar hematocrit elevation at the downstream region with 45%-H_ct in the same 10 μm microvessel is also observed with the cells randomly located. In 20 μm microvessels with 45%-H_ct, the Pf-IRBCs slow down the velocity of the healthy red blood cells (HRBCs) around them and then locally elevate the volume fraction and result in the accumulation of the RBCs at the center of the vessels, thus leaving a thicker cell free layer (CFL) near the vessel wall than normal. Variation of wall shear stress (WSS) is caused by the fluctuation of local H_ct and the distance between the wall and the RBCs. Moreover, in high-hematocrit condition (45%), malaria-infected cells have a tendency to migrate to the edge of the aggregates which is due to the uninterrupted hydrodynamic interaction between the HRBCs and Pf-IRBC. Our results suggest that the existence of Pf-IRBCs is a nonnegligible factor for the fluctuation of hematocrit and WSS and also contributes to the increase of CFL of pathological blood flow in microvessels. The numerical approach presented has the potential to be utilized to RBC disorders and other hematologic diseases.

Microfluidics for investigating vaso-occlusions in sickle cell disease

SCD stems from amutation in the beta globin gene. Upon deoxygenation, hemoglobin polymerizes and triggers RBC remodeling. This phenomenon is central to SCD pathogenesis as individuals suffering from the disease are plagued by painful vaso-occlusive crises episodes. These episodes are the result of a combination of processes including inflammation, thrombosis, and blood cell adhesion to the vascular wall which leads to blockages within the vasculature termed vaso-occlusions. Vaso-occlusive episodes deprive tissues of oxygen and are a major contributor to SCD-related complications; unfortunately, the complex mechanisms that contribute to vaso-occlusions are not well understood. Vaso-occlusions can occur in post-capillary venules; hence, the microvasculature is a prime target for SCD therapies. Traditional in vitro systems poorly recapitulate architectural and dynamic flow properties of in vivo systems. However, microfluidic devices can capture features of the native vasculature such as cellular composition, flow, geometry, and ECM presentation. This review, although not comprehensive, highlights microfluidic approaches that aim to improve our current understanding of the pathophysiological mechanisms surrounding SCD. Microfluidic platforms can aid in identifying factors that may contribute to disease severity and can serve as suitable test beds for novel treatment strategies which may improve patient outcomes.

Probing eukaryotic cell mechanics via mesoscopic simulations

Cell mechanics has proven to be important in many biological processes. Although there is a number of experimental techniques which allow us to study mechanical properties of cell, there is still a lack of understanding of the role each sub-cellular component plays during cell deformations. We present a new mesoscopic particle-based eukaryotic cell model which explicitly describes cell membrane, nucleus and cytoskeleton. We employ Dissipative Particle Dynamics (DPD) method that provides us with the unified framework for modeling of a cell and its interactions in the flow. Data from micropipette aspiration experiments were used to define model parameters. The model was validated using data from microfluidic experiments. The validated model was then applied to study the impact of the sub-cellular components on the cell viscoelastic response in micropipette aspiration and microfluidic experiments.

Mesoscopic Adaptive Resolution Scheme toward Understanding of Interactions between Sickle Cell Fibers

Understanding of intracellular polymerization of sickle hemoglobin (HbS) and subsequent interaction with the membrane of a red blood cell (RBC) is important to predict the altered morphologies and mechanical properties of sickle RBCs in sickle cell anemia. However, modeling the integrated processes of HbS nucleation, polymerization, HbS fiber interaction, and subsequent distortion of RBCs is challenging as they occur at multispatial scales, ranging from nanometers to micrometers. To make progress toward simulating the integrated processes, we propose a hybrid HbS fiber model, which couples fine-grained and coarse-grained HbS fiber models through a mesoscopic adaptive resolution scheme (MARS). To this end, we apply a microscopic model to capture the dynamic process of polymerization of HbS fibers, while maintaining the mechanical properties of polymerized HbS fibers by the mesoscopic model, thus providing a means of bridging the subcellular and cellular phenomena in sickle cell disease. At the subcellular level, this model can simulate HbS polymerization with preexisting HbS nuclei. At the cellular level, if combined with RBC models, the generated HbS fibers could be applied to study the morphologies and membrane stiffening of sickle RBCs. One important feature of the MARS is that it can be easily employed in other particle-based multiscale simulations where a dynamic coarse-graining and force-blending method is required. As demonstrations, we first apply the hybrid HbS fiber model to simulate the interactions of two growing fibers and find that their final configurations depend on the orientation and interaction distance between two fibers, in good agreement with experimental observations. We also model the formation of fiber bundles and domains so that we explore the mechanism that causes fiber branching.

Modeling of Biomechanics and Biorheology of Red Blood Cells in Type 2 Diabetes Mellitus

Erythrocytes in patients with type-2 diabetes mellitus (T2DM) are associated with reduced cell deformability and elevated blood viscosity, which contribute to impaired blood flow and other pathophysiological aspects of diabetes-related vascular complications. In this study, by using a two-component red blood cell (RBC) model and systematic parameter variation, we perform detailed computational simulations to probe the alteration of the biomechanical, rheological, and dynamic behavior of T2DM RBCs in response to morphological change and membrane stiffening. First, we examine the elastic response of T2DM RBCs subject to static tensile forcing and their viscoelastic relaxation response upon release of the stretching force. Second, we investigate the membrane fluctuations of T2DM RBCs and explore the effect of cell shape on the fluctuation amplitudes. Third, we subject the T2DM RBCs to shear flow and probe the effects of cell shape and effective membrane viscosity on their tank-treading movement. In addition, we model the cell dynamic behavior in a microfluidic channel with constriction and quantify the biorheological properties of individual T2DM RBCs. Finally, we simulate T2DM RBC suspensions under shear and compare the predicted viscosity with experimental measurements. Taken together, these simulation results and their comparison with currently available experimental data are helpful in identifying a specific parametric model-the first of its kind, to our knowledge-that best describes the main hallmarks of T2DM RBCs, which can be used in future simulation studies of hematologic complications of T2DM patients.

Method for quantitative assessment of retinal vessel tortuosity in optical coherence tomography angiography applied to sickle cell retinopathy

Tortuosity is an important geometric vessel parameter and among the first microvascular alterations observed in various retinopathies. In the current study, a quantitative vessel tortuosity index (VTI) based on a combination of local and global centerline features is presented. Performance of VTI and previously established tortuosity indices were compared against human observers' evaluation of tortuosity. An image-processing pipeline was developed for application of VTI in retinal vessels imaged by optical coherence tomography angiography (OCTA) in perifoveal (6 mm × 6 mm) and parafoveal (3 mm × 3 mm) regions centered on the fovea. Forty-one subjects (12 healthy control (NC) and 29 sickle cell retinopathy (SCR)) and 10 subjects (5 NC and 5 SCR) were imaged in the perifoveal and parafoveal regions, respectively. The relationship between VTI and age was examined in the perifoveal regions in NC subjects. VTI was measured from the OCTA images and compared between NC and SCR subjects using generalized least square regression with and without adjusting for age and race. VTI was found to correlate better than the 4 previous indices with performance of human observers. In the perifoveal region, a significant correlation was observed between VTI and age (r = -0.4, P<0.001, N = 12). VTI was higher in SCR than NC subjects in perifoveal and parafoveal regions (P≤0.001). The results demonstrate that the proposed method shows promise for detection of increased tortuosity in vessels due to retinal disorders.

Probing the Twisted Structure of Sickle Hemoglobin Fibers via Particle Simulations

Polymerization of sickle hemoglobin (HbS) is the primary pathogenic event of sickle cell disease. For insight into the nature of the HbS polymer fiber formation, we develop a particle model-resembling a coarse-grained molecular model-constructed to match the intermolecular contacts between HbS molecules. We demonstrate that the particle model predicts the formation of HbS polymer fibers by attachment of monomers to rough fiber ends and the growth rate increases linearly with HbS concentration. We show that the characteristic 14-molecule fiber cross section is preserved during growth. We also correlate the asymmetry of the contact sites on the HbS molecular surface with the structure of the polymer fiber composed of seven helically twisted double strands. Finally, we show that the same asymmetry mediates the mechanical and structural properties of the HbS polymer fiber.

Patient-specific modeling of individual sickle cell behavior under transient hypoxia

Sickle cell disease (SCD) is a highly complex genetic blood disorder in which red blood cells (RBC) exhibit heterogeneous morphology changes and decreased deformability. We employ a kinetic model for cell morphological sickling that invokes parameters derived from patient-specific data. This model is used to investigate the dynamics of individual sickle cells in a capillary-like microenvironment in order to address various mechanisms associated with SCD. We show that all RBCs, both hypoxia-unaffected and hypoxia-affected ones, regularly pass through microgates under oxygenated state. However, the hypoxia-affected cells undergo sickling which significantly alters cell dynamics. In particular, the dense and rigid sickle RBCs are obstructed thereby clogging blood flow while the less dense and deformable ones are capable of circumnavigating dead (trapped) cells ahead of them by choosing a serpentine path. Informed by recent experiments involving microfluidics that provide in vitro quantitative information on cell dynamics under transient hypoxia conditions, we have performed detailed computational simulations of alterations to cell behavior in response to morphological changes and membrane stiffening. Our model reveals that SCD exhibits substantial heterogeneity even within a particular density-fractionated subpopulation. These findings provide unique insights into how individual sickle cells move through capillaries under transient hypoxic conditions, and offer novel possibilities for designing effective therapeutic interventions for SCD.

Sickle cell disease is a genetic blood disease that causes vaso-occlusive pain crises. Here, we investigate the individual sickle cell behavior under controlled hypoxic conditions through patient-specific predictive computational simulations that are informed by companion microfluidic experiments. We identify the different dynamic behavior between individual sickle RBCs and normal ones in microfluidic flow, and analyze the hypoxia-induced alteration in individual cell behavior and single-cell capillary obstruction under physiological conditions.

Measuring sickle cell morphology during blood flow

During a sickle cell crisis in sickle cell anemia patients, deoxygenated red blood cells may change their mechanical properties and block small blood vessels, causing pain, local tissue damage, and possibly organ failure. Measuring the structural and morphological changes in sickle cells is important for understanding the factors contributing to vessel blockage and for developing an effective treatment. In this work, we image blood cells from sickle cell anemia patients using spectrally encoded flow cytometry, and analyze the interference patterns between reflections from the cell membranes. Using a numerical simulation for calculating the interference pattern obtained from a model of a red blood cell, we propose an analytical expression for the three-dimensional shape of characteristic sickle cells and compare our results to a previously suggested model. Our imaging approach offers new means for analyzing the morphology of sickle cells, and could be useful for studying their unique physiological and biomechanical properties.

Conjunctival microvascular hemodynamics following vaso-occlusive crisis in sickle cell disease

Painful vaso-occlusive crisis (VOC) is the clinical hallmark of sickle cell disease (SCD). Microcirculatory hemodynamic changes following painful VOC may be indicative of future development of VOC events in subjects with SCD. The purpose of the present study was to determine alterations in conjunctival microvascular hemodynamics during non-crisis state in SCD subjects with a history of VOC. Conjunctival microcirculation imaging was performed to measure conjunctival diameter (D) and axial blood velocity (V) in 10 control and 30 SCD subjects. SCD subjects were categorized into two groups based on their history of VOC within a 2-year period before imaging (with or without VOC-H) and also based on whether there was progression in the rate of VOCs during a 2-year period following imaging as compared to before imaging (with or without VOC-P). Conjunctival V was significantly higher in SCD subjects with VOC-H than in both control subjects and SCD subjects without VOC-H (P≤0.03). Conjunctival V was also significantly higher in SCD subjects with VOC-P compared with control subjects and SCD subjects without VOC-P (P≤0.03). Assessment of the conjunctival microcirculation may be useful for understanding hemodynamic changes that lead to VOC events in SCD subjects.

Biomechanics and biorheology of red blood cells in sickle cell anemia

Sickle cell anemia (SCA) is an inherited blood disorder that causes painful crises due to vaso-occlusion of small blood vessels. The primary cause of the clinical phenotype of SCA is the intracellular polymerization of sickle hemoglobin resulting in sickling of red blood cells (RBCs) in deoxygenated conditions. In this review, we discuss the biomechanical and biorheological characteristics of sickle RBCs and sickle blood as well as their implications toward a better understanding of the pathophysiology and pathogenesis of SCA. Additionally, we highlight the adhesive heterogeneity of RBCs in SCA and their specific contribution to vaso-occlusive crisis.

Dynamic and rheological properties of soft biological cell suspensions

Quantifying dynamic and rheological properties of suspensions of soft biological particles such as vesicles, capsules, and red blood cells (RBCs) is fundamentally important in computational biology and biomedical engineering. In this review, recent studies on dynamic and rheological behavior of soft biological cell suspensions by computer simulations are presented, considering both unbounded and confined shear flow. Furthermore, the hemodynamic and hemorheological characteristics of RBCs in diseases such as malaria and sickle cell anemia are highlighted.

Patient-specific blood rheology in sickle-cell anaemia

Sickle-cell anaemia (SCA) is an inherited blood disorder exhibiting heterogeneous cell morphology and abnormal rheology, especially under hypoxic conditions. By using a multiscale red blood cell (RBC) model with parameters derived from patient-specific data, we present a mesoscopic computational study of the haemodynamic and rheological characteristics of blood from SCA patients with hydroxyurea (HU) treatment (on-HU) and those without HU treatment (off-HU). We determine the shear viscosity of blood in health as well as in different states of disease. Our results suggest that treatment with HU improves or worsens the rheological characteristics of blood in SCA depending on the degree of hypoxia. However, on-HU groups always have higher levels of haematocrit-to-viscosity ratio (HVR) than off-HU groups, indicating that HU can indeed improve the oxygen transport potential of blood. Our patient-specific computational simulations suggest that the HVR level, rather than the shear viscosity of sickle RBC suspensions, may be a more reliable indicator in assessing the response to HU treatment.

Efficient Schmidt number scaling in dissipative particle dynamics

Dissipative particle dynamics is a widely used mesoscale technique for the simulation of hydrodynamics (as well as immersed particles) utilizing coarse-grained molecular dynamics. While the method is capable of describing any fluid, the typical choice of the friction coefficient γ and dissipative force cutoff rc yields an unacceptably low Schmidt number Sc for the simulation of liquid water at standard temperature and pressure. There are a variety of ways to raise Sc, such as increasing γ and rc, but the relative cost of modifying each parameter (and the concomitant impact on numerical accuracy) has heretofore remained undetermined. We perform a detailed search over the parameter space, identifying the optimal strategy for the efficient and accuracy-preserving scaling of Sc, using both numerical simulations and theoretical predictions. The composite results recommend a parameter choice that leads to a speed improvement of a factor of three versus previously utilized strategies.

Changes in Conjunctival Hemodynamics Predict Albuminuria in Sickle Cell Nephropathy

BACKGROUND

Albuminuria is an early manifestation of deterioration in renal function in subjects with sickle cell disease (SCD). Hyperfiltration may be an early mechanism for kidney damage in SCD. The purpose of the current study was to determine the association between conjunctival hemodynamics and albuminuria in SCD subjects with preserved glomerular filtration rate.

METHODS

Conjunctival microcirculation imaging was performed to measure conjunctival diameter and axial blood velocity (V) in 35 SCD and 10 healthy control subjects. Albuminuria, defined as albumin excretion ratio (AER), was obtained from the medical charts. Based on the 95% CI of conjunctival V in control subjects (0.40-0.60 mm/s), SCD subjects were allocated to 3 groups: V1 <0.40 mm/s (n = 7), V2 of 0.40-0.60 mm/s (n = 18) and V3 ≥0.60 mm/s (n = 10).

RESULTS

Mean log(AER) measurements in the V1, V2 and V3 groups were 1.08 ± 0.67, 1.39 ± 0.59 and 2.00 ± 0.91 mg/g creatinine, respectively, and followed a positive linear trend from the V1 to V3 groups (p = 0.01). By multivariate linear regression analysis, conjunctival V significantly correlated with albuminuria (p = 0.01) independent of age, blood pressure, α-thalassemia, hematocrit, white blood cell count and lactate dehydrogenase concentration.

CONCLUSIONS

Increased conjunctival V is associated with albuminuria in SCD subjects. Assessment of conjunctival microvascular hemodynamics may improve our understanding of the pathophysiology and clinical management of sickle cell nephropathy.

Multi-scale biological and physical modelling of the tumour micro-environment

Paced by advances in high performance computing, and algorithms for multi-physics and multi-scale simulation, a number of groups have recently established numerical models of flowing blood systems, where cell-scale interactions are explicitly resolved. To be biologically representative, these models account for some or all of: (1) fluid dynamics of the carrier flow, (2) structural dynamics of the cells and vessel walls, (3) interaction and transport biochemistry, and, (4) methods for scaling to physiologically representative numbers of cells. In this article, our interest is the modelling of the tumour micro-environment. We review the broader area of cell-scale resolving blood flow modelling, while focusing on the particular interactions of tumour cells and white blood cells, known to play an important role in metastasis.

Conjunctival microvascular haemodynamics in sickle cell retinopathy

PURPOSE

To determine alterations in bulbar conjunctival microvascular haemodynamics in sickle cell retinopathy (SCR) subjects with focal macular thinning (FMT).

METHODS

Conjunctival microcirculation imaging and spectral domain optical coherence tomography (SD-OCT) were performed in 22 subjects (eyes) diagnosed with SCR. Based on evaluation of SD-OCT retinal thickness maps, eyes were assigned to one of the two groups: with or without FMT. Conjunctival venular diameter and axial blood velocity were measured in multiple venules in each eye by customized image analysis algorithms. Measurements were then categorized into two vessel size groups (vessel size 1 and 2) and compared between FMT groups. A Pearson correlation coefficient was computed to assess the relationship between retinal thickness and axial blood velocity.

RESULTS

Mean age, haematocrit, sickle cell haemoglobin type and median retinopathy score were not significantly different between the two groups (p ≥ 0.1). Retinal thickness in parafoveal and perifoveal temporal subfields was significantly lower in eyes with FMT as compared to eyes without FMT (p ≤ 0.04). There was a significant effect of FMT on axial blood velocity (p = 0.04), while the effect of vessel size was not significant (p = 0.4). In vessel size 1, axial blood velocity was lower in eyes with FMT than in eyes without FMT (p = 0.03), while in vessel size 2, there was no statistically significant difference between FMT groups (p = 0.1). In vessel size 1, there was a significant positive correlation between axial blood velocity and retinal thickness in the perifoveal (r = 0.48, p = 0.02) and parafoveal (r = 0.43, p = 0.04) temporal subfields.

CONCLUSION

Conjunctival axial blood velocity in small venules is reduced in SCR subjects with focal macular thinning.

A microfluidic device to sort capsules by deformability: a numerical study

Guided by extensive numerical simulations, we propose a microfluidic device that can sort elastic capsules by their deformability. The device consists of a duct embedded with a semi-cylindrical obstacle, and a diffuser which further enhances the sorting capability. We demonstrate that the device can operate reasonably well under changes in the initial position of the capsule. The efficiency of the device remains essentially unaltered under small changes of the obstacle shape (from semi-circular to semi-elliptic cross-section). Confinement along the direction perpendicular to the plane of the device increases its efficiency. This work is the first numerical study of cell sorting by a realistic microfluidic device.

Phase diagrams and morphological evolution in wrapping of rod-shaped elastic nanoparticles by cell membrane: a two-dimensional study

A fundamental understanding of cell-nanomaterial interaction is essential for biomedical diagnostics, therapeutics, and nanotoxicity. Here, we perform a theoretical analysis to investigate the phase diagram and morphological evolution of an elastic rod-shaped nanoparticle wrapped by a lipid membrane in two dimensions. We show that there exist five possible wrapping phases based on the stability of full wrapping, partial wrapping, and no wrapping states. The wrapping phases depend on the shape and size of the particle, adhesion energy, membrane tension, and bending rigidity ratio between the particle and membrane. While symmetric morphologies are observed in the early and late stages of wrapping, in between a soft rod-shaped nanoparticle undergoes a dramatic symmetry breaking morphological change while stiff and rigid nanoparticles experience a sharp reorientation. These results are of interest to the study of a range of phenomena including viral budding, exocytosis, as well as endocytosis or phagocytosis of elastic particles into cells.

Haemolysis and abnormal haemorheology in sickle cell anaemia

Although pulmonary hypertension, leg ulcers, priapism, stroke and glomerulopathy in sickle cell anaemia (SCA) result from the adverse effects of chronic haemolysis on vascular function (haemolytic phenotype), osteonecrosis, acute chest syndrome and painful vaso-occlusive crises are caused by abnormal vascular cell adhesion and increased blood viscosity (viscosity-vaso-occlusion phenotype). However, this model with two sub-phenotypes does not take into account the haemorheological dimension. We tested the relationships between the biological parameters reflecting the haemolytic rate (haemolytic component) and red blood cell (RBC) rheological characteristics in 97 adults with SCA. No significant difference in the proportion of patients with low or high haemolytic component in the low and high blood viscosity groups was observed. The RBC elongation index (i.e. deformability) was negatively correlated with the haemolytic component. The RBC aggregates strength (i.e. RBC aggregates robustness) was negatively correlated with RBC elongation index. Sickle RBCs with high density had lower elongation index and higher aggregates strength. In conclusion, (i) the 'haemolytic' phenotype is characterized by decreased RBC deformability and increased RBC aggregates strength and (ii) the viscosity-vaso-occlusive phenotype is characterized by increased RBC deformability but not always by increased blood viscosity. α-thalassaemia modulates the haemorheological properties but other factors seem to be involved.

Cellular adhesion and the endothelium: P-selectin

P-selectin on endothelial cell surfaces is central to impaired microvascular blood flow in sickle cell disease (SCD). Restoration of blood flow is expected to provide therapeutic benefit for SCD patients, whatever the mechanism of action of the treatment. Long-term oral administration of a P-selectin-blocking agent potentially improves blood flow and averts acute painful vaso-occlusive crises in patients with SCD. This review focuses on the pathophysiology of the impairment of microvascular blood flow in SCD with an emphasis on the role of P-selectin and summarizes the status of development of antiselectin therapies as a means of improving microvascular flow.

A systems approach to blood disorders

A systems approach to blood diseases can help make essential contributions to our ability to diagnose, treat, and perhaps even prevent common diseases in humans. Using blood as a window, one can study health and disease through this unique tool box with reactive biological fluids that mirrors the prevailing hemodynamics of the vessel walls and the various blood cell types. Many blood diseases, rare and common, can and have been exploited using systems biology approaches with successful results and therefore ideal models for systems medicine. More importantly, hematopoiesis offers one of the best studied systems with insight into stem cell biology, cellular interaction, development; linage programming and reprogramming that are influenced every day by the most mature and understood regulatory networks.

Computational biorheology of human blood flow in health and disease

Hematologic disorders arising from infectious diseases, hereditary factors and environmental influences can lead to, and can be influenced by, significant changes in the shape, mechanical and physical properties of red blood cells (RBCs), and the biorheology of blood flow. Hence, modeling of hematologic disorders should take into account the multiphase nature of blood flow, especially in arterioles and capillaries. We present here an overview of a general computational framework based on dissipative particle dynamics (DPD) which has broad applicability in cell biophysics with implications for diagnostics, therapeutics and drug efficacy assessments for a wide variety of human diseases. This computational approach, validated by independent experimental results, is capable of modeling the biorheology of whole blood and its individual components during blood flow so as to investigate cell mechanistic processes in health and disease. DPD is a Lagrangian method that can be derived from systematic coarse-graining of molecular dynamics but can scale efficiently up to arterioles and can also be used to model RBCs down to the spectrin level. We start from experimental measurements of a single RBC to extract the relevant biophysical parameters, using single-cell measurements involving such methods as optical tweezers, atomic force microscopy and micropipette aspiration, and cell-population experiments involving microfluidic devices. We then use these validated RBC models to predict the biorheological behavior of whole blood in healthy or pathological states, and compare the simulations with experimental results involving apparent viscosity and other relevant parameters. While the approach discussed here is sufficiently general to address a broad spectrum of hematologic disorders including certain types of cancer, this paper specifically deals with results obtained using this computational framework for blood flow in malaria and sickle cell anemia.

Human bulbar conjunctival hemodynamics in hemoglobin SS and SC disease

The known biophysical variations of hemoglobin (Hb) S and Hb C may result in hemodynamic differences between subjects with SS and SC disease. The purpose of this study was to measure and compare conjunctival hemodynamics between subjects with Hb SS and SC hemoglobinopathies. Image sequences of the conjunctival microcirculation were acquired in 9 healthy control subjects (Hb AA), 24 subjects with SC disease, and 18 subjects with SS disease, using a prototype imaging system. Diameter (D) and blood velocity (V) measurements were obtained in multiple venules of each subject. Data were categorized according to venule caliber by averaging V and D for venules with diameters less than (vessel size 1) or greater than (vessel size 2) 15 µm. V in vessel size 2 was significantly greater than V in vessel size 1 in the AA and SS groups (P ≥ 0.009), but not in the SC group (P = 0.1). V was significantly lower in the SC group as compared to the SS group (P = 0.03). In AA and SS groups, V correlated with D (P ≤ 0.005), but the correlation was not statistically significant in the SC group (P = 0.08). V was inversely correlated with hematocrit in the SS group for large vessels (P = 0.03); however, no significant correlation was found in the SC group (P ≥ 0.2). Quantitative assessment of conjunctival microvascular hemodynamics in SS and SC disease may advance understanding of sickle cell disease pathophysiology and thereby improve therapeutic interventions.

Probing vasoocclusion phenomena in sickle cell anemia via mesoscopic simulations

Vasoocclusion crisis is a key hallmark of sickle cell anemia. Although early studies suggest that this crisis is caused by blockage of a single elongated cell, recent experiments have revealed that vasoocclusion is a complex process triggered by adhesive interactions among different cell groups in multiple stages. However, the quantification of the biophysical characteristics of sickle cell anemia remains an open issue. Based on dissipative particle dynamics, we develop a multiscale model for the sickle red blood cells (SS-RBCs), accounting for diversity in both shapes and cell rigidities, to investigate the precise mechanism of vasoocclusion. First, we investigate the adhesive dynamics of a single SS-RBC in shear flow and static conditions, and find that the different cell groups (SS2: young-deformable SS-RBCs, ISCs: rigid-irreversible SS-RBCs) exhibit heterogeneous adhesive behavior due to the diverse cell morphologies and membrane rigidities. We quantify the observed adhesion behavior (in static conditions) in terms of a balance of free energies due to cell adhesion and deformation, and propose a power law that relates the free-energy increase as a function of the contact area. We further simulate postcapillary flow of SS-RBC suspensions with different cell fractions. The more adhesive SS2 cells interact with the vascular endothelium and trap ISC cells, resulting in vasoocclusion in vessels less than 12-14 μm depending on the hematocrit. Under inflammation, adherent leukocytes may also trap ISC cells, resulting in vasoocclusion in even larger vessels.

Multiscale modeling of blood flow: from single cells to blood rheology

Mesoscale simulations of blood flow, where the red blood cells are described as deformable closed shells with a membrane characterized by bending rigidity and stretching elasticity, have made much progress in recent years to predict the flow behavior of blood cells and other components in various flows. To numerically investigate blood flow and blood-related processes in complex geometries, a highly efficient simulation technique for the plasma and solutes is essential. In this review, we focus on the behavior of single and several cells in shear and microcapillary flows, the shear-thinning behavior of blood and its relation to the blood cell structure and interactions, margination of white blood cells and platelets, and modeling hematologic diseases and disorders. Comparisons of the simulation predictions with existing experimental results are made whenever possible, and generally very satisfactory agreement is obtained.

Effect of chain chirality on the self-assembly of sickle hemoglobin

We present simulation results on the self-assembly behavior of sickle hemoglobin (HbS). A coarse-grained HbS model, which contains hydrophilic and hydrophobic particles explicitly, is constructed to match the structural properties and physical description of HbS. The hydrophobic interactions are shown to be necessary with chirality being the main driver for the formation of HbS fibers. In the absence of chain chirality, only small self-assembled aggregates are observed whereas self-assembled elongated steplike bundle microstructures appear when we include chain chirality. We also investigate the effect of confinement on self-assembly, and find that elongated fibers-similar to open-space ones-can be obtained in hard confinement domains but cannot be formed within compliant red blood cell (RBC) domains under the same assumptions. We show, however, that by placing explicitly HbS fibers inside the RBCs and subjecting them to linear elongation and bending, we obtain different types of sickle-shaped RBCs as observed in sickle cell anemia.

Continuum- and particle-based modeling of shapes and dynamics of red blood cells in health and disease

We review recent advances in multiscale modeling of the mechanics of healthy and diseased red blood cells (RBCs), and blood flow in the microcirculation. We cover the traditional continuum-based methods but also particle-based methods used to model both the RBCs and the blood plasma. We highlight examples of successful simulations of blood flow including malaria and sickle cell anemia.