Volume Fraction Of Red Blood Cells Research Articles

Early stage of erythrocyte sedimentation rate test: Fracture of a high-volume-fraction gel.

Erythrocyte sedimentation rate (ESR) is a clinical parameter used as a nonspecific marker for inflammation, and recent studies have shown that it is linked to the collapse of the gel formed by red blood cells (RBCs) at physiological hematocrits (i.e. RBC volume fraction). Previous research has suggested that the observation of a slower initial dynamics is related to the formation of fractures in the gel. Moreover, RBC gels present specific properties due to the anisotropic shape and flexibility of the RBCs. Namely, the onset of the collapse is reached earlier and the settling velocity of the gel increases with increasing attraction between the RBCs, while the gel of spherical particles shows the opposite trend. Here, we report experimental observations of the gel structure during the onset of the collapse. We suggest an equation modeling this initial process as fracturing of the gel. We demonstrate that this equation provides a model for the motion of the interface between blood plasma and the RBC gel, along the whole time span. We also observe that the increase in the attraction between the RBCs modifies the density of fractures in the gel, which explains why the gel displays an earlier onset when the aggregation energy between the RBCs increases. Our work uncovers the detailed physical mechanism underlying the ESR and provides insights into the fracture dynamics of an RBC gel. These results can improve the accuracy of clinical measurements.

Multiphase Flow Hemodynamic Evaluation of Vertebral Artery Stenosis Lesions and Plaque Stability.

Atherosclerosis is one of the main causes of vertebral artery stenosis, which reduces blood supply to the posterior circulation, resulting in cerebral infarction or death. To investigate stenosis rates and locations on the development of vertebral artery plaques. Stenosis models with varying degrees and positions of stenosis were established. The stenosis area was comprehensively analyzed using multiphase flow numerical simulation. Wall shear stress (WSS), blood flow velocity, and red blood cell (RBC) volume fraction were calculated. Blood flow velocity in 30-70% stenosis of each segment tended to increase significantly higher than normal. Downstream of 50% stenosis exhibited turbulent flow; downstream of 70% displayed reflux. Severe stenosis increases the WSS and distribution area. The mixed area of high and low WSS appeared downstream of the stenosis. The RBC volume fraction at the stenosis increased (maximum value: 0.487 at 70% stenosis in the V4), which was 1.08 times the normal volume fraction. Turbulent and backflow regions exhibited complex RBC volume fraction distributions. Flow velocity, WSS, and RBC volume fraction at the stenosis increase with stenosis severity, increasing plaque shedding. Narrow downstream spoiler and reflux areas possess low WSS and high erythrocyte volume fractions, accelerating plaque growth.

Red blood cell lingering modulates hematocrit distribution in the microcirculation

The distribution of red blood cells (RBCs) in the microcirculation determines the oxygen delivery and solute transport to tissues. This process relies on the partitioning of RBCs at successive bifurcations throughout the microvascular network, and it has been known since the last century that RBCs partition disproportionately to the fractional blood flow rate, therefore leading to heterogeneity of the hematocrit (i.e., volume fraction of RBCs in blood) in microvessels. Usually, downstream of a microvascular bifurcation, the vessel branch with a higher fraction of blood flow receives an even higher fraction of RBC flux. However, both temporal and time-average deviations from this phase-separation law have been observed in recent studies. Here, we quantify how the microscopic behavior of RBC lingering (i.e., RBCs temporarily residing near the bifurcation apex with diminished velocity) influences their partitioning, through combined in vivo experiments and in silico simulations. We developed an approach to quantify the cell lingering at highly confined capillary-level bifurcations and demonstrate that it correlates with deviations of the phase-separation process from established empirical predictions by Pries et al. Furthermore, we shed light on how the bifurcation geometry and cell membrane rigidity can affect the lingering behavior of RBCs; e.g., rigid cells tend to linger less than softer ones. Taken together, RBC lingering is an important mechanism that should be considered when studying how abnormal RBC rigidity in diseases such as malaria and sickle-cell disease could hinder the microcirculatory blood flow or how the vascular networks are altered under pathological conditions (e.g., thrombosis, tumors, aneurysm).

Tangential flow filtration facilitated washing of human red blood cells: A proof-of-concept study.

Red blood cell (RBC) units in hypothermic storage degrade over time, commonly known as the RBC storage lesion. These older RBC units can cause adverse clinical effects when transfused, as older RBCs in the unit lyse and release cell-free haemoglobin (Hb), a potent vasodilator that can elicit vasoconstriction, systemic hypertension and oxidative tissue injury after transfusion. In this study, we examined a novel method of washing ex vivo stored single RBC units to remove accumulated cellular waste, specifically cell-free Hb, using tangential flow filtration (TFF) driven by a centrifugal pump. The TFF RBC washing system was run under hypothermic conditions at 4°C, at a constant system volume with 0.9wt% saline as the wash solution. The RBC washing process was conducted on 10 separate RBC units. For this proof-of-concept study, RBC units were expired at the time of washing (60-70 days old). Cell-free Hb was quantified by UV-visible absorbance spectroscopy and analysed via the Winterbourn equations. Pre- and post-wash RBC samples were analysed by Hemox Analyser, Coulter counter and Brookfield rheometer. The RBC volume fraction in solution was measured throughout the wash process by standard haematocrit (HCT) analysis. No substantial decrease in the HCT was observed during the TFF RBC washing process. However, there was a significant decrease in RBC concentration in the first half of the TFF RBC wash process, with no significant change in RBC concentration during the second half of the TFF cell wash process with an 87% overall cell recovery compared with the total number of cells before initiation of cell washing. Utilization of the extinction coefficients and characteristic peaks of each Hb species potentially present in solution was quantified by Winterbourn analysis on retentate and permeate samples for each diacycle to quantify Hb concentration during the washing process. Significant cell-free Hb reduction was observed within the first four diacycles with a starting cell-free Hb concentration in the RBC unit of 0.105 mM, which plateaus to a constant Hb concentration of 0.01 mM or a total extracellular Hb mass of 0.2g in the resultant washed unit. The oxygen equilibrium curve showed a significant decrease in P50 between the initial and final RBC sample cell wash with an initial P50 of 15.6 ± 1.8 mm Hg and a final P50 of 14 ± 1.62 mm Hg. Cooperativity increased after washing from an initial Hill coefficient of 2.37 ± 0.19 compared with a final value of 2.52 ± 0.12. Overall, this study investigated the proof-of-concept use of TFF for washing single RBC units with an emphasis on the removal of cell-free Hb from the unit. Compared with traditional cell washing procedures, the designed system was able to more efficiently remove extracellular Hb but resulted in longer wash times. For a more complete investigation of the TFF RBC washing process, further work should be done to investigate the effects of RBC unit storage after washing. The designed system is lightweight and transportable with the ability to maintain sterility between uses, providing a potential option for bedside ex vivo transfusion in clinical applications.

Numerical simulation of blood flow modeled as a fluid- particulate mixture

ABSTRACT A continuum model for the transport of red blood cells (RBC) inside arteries and capillaries of small diameters is proposed. The pressure and velocity fields are solved using the Navier-Stokes equations while the distribution of the RBC volume fraction, namely, hematocrit is obtained by solving the particle transport equation arising from the diffusive flux model. The momentum and hematocrit transport equations are coupled through a hematocrit-dependent blood viscosity model. The coupled equations are numerically solved using a 3D unstructured finite volume method. The proposed model predicts the shear induced diffusion of RBCs where RBCs migrate from the wall to the center of the blood vessel leading to a cell free layer (CFL) near the wall. Three geometries with sizes of the order of 40 µm have been considered for the present work. For flow inside a tube, results in terms of the concentration distribution and cell-free layer from the present continuum model show a good match with experiments and DPD simulations. For flow inside a tube with a constriction it is found that hematocrit depletion is greater downstream of the neck of the constriction. In addition, the effect of hematocrit loading on its distribution is correctly predicted. Finally, for a flow inside a tube with a bifurcation the average hematocrit concentration is found to be higher for the branch with the higher flow rate, thereby complying with the well-known bifurcation law.

Numerical simulation of two-phase non-Newtonian blood flow with fluid-structure interaction in aortic dissection

The behavior of blood cells and vessel compliance significantly influence hemodynamic parameters, which are closely related to the development of aortic dissection. Here the two-phase non-Newtonian model and the fluid-structure interaction (FSI) method are coupled to simulate blood flow in a patient-specific dissected aorta. Moreover, three-element Windkessel model is applied to reproduce physiological pressure waves. Important hemodynamic indicators, such as the spatial distribution of red blood cells (RBCs) and vessel wall displacement, which greatly influence the hemodynamic characteristics are analyzed. Results show that the proximal false lumen near the entry tear appears to be a vortex zone with a relatively lower volume fraction of RBCs, a low time-averaged wall shear stress (TAWSS) and a high oscillatory shear index (OSI), providing a suitable physical environment for the formation of atherosclerosis. The highest TAWSS is located in the narrow area of the distal true lumen which might cause further dilation. TAWSS distributions in the FSI model and the rigid wall model show similar trend, while there is a significant difference for the OSI distributions. We suggest that an integrated model is essential to simulate blood flow in a more realistic physiological environment with the ultimate aim of guiding clinical treatment.

Optimal cell transport in straight channels and networks

Flux of rigid or soft particles (such as drops, vesicles, red blood cells, etc.) in a channel is a complex function of particle concentration, which depends on the details of induced dissipation and suspension structure due to hydrodynamic interactions with walls or between neighboring particles. Through two-dimensional and three-dimensional simulations and a simple model that reveals the contribution of the main characteristics of the flowing suspension, we discuss the existence of an optimal volume fraction for cell transport and its dependence on the cell mechanical properties. The example of blood is explored in detail, by adopting the commonly used modeling of red blood cells dynamics. We highlight the complexity of optimization at the level of a network, due to the antagonist evolution of local volume fraction and optimal volume fraction with the channels diameter. In the case of the blood network, the most recent results on the size evolution of vessels along the circulatory network of healthy organs suggest that the red blood cell volume fraction (hematocrit) of healthy subjects is close to optimality, as far as transport only is concerned. However, the hematocrit value of patients suffering from diverse red blood cel pathologies may strongly deviate from optimality.

Analysis of Hematocrit Variation Induced by Malaria-infected Red Blood Cells

The rheological properties of red blood cells (RBCs) in microvessels have a significant impact on the flow and transport of oxygen and nutrients in the blood. This paper used numerical methods to simulate the rheological property of the malaria-infected cells in microvessel, and compare the simulation results with other people’s findings. The results illustrate that in the 10-μm microvessel with low hematocrit (Hct) condition (18% and 27%), the Plasmodium falciparum-infected red blood cells (Pf-IRBCs) and healthy red blood cells (HRBCs) first form a “train”. In addition, the velocity of the Pf-IRBCs in the microvascular flow is slower than HRBCs, resulting in the increase of the surrounding erythrocyte hematocrit to about 40% or more. But this increase of volume fraction of RBCs is just temporary. It is observed that a similar phenomenon happens at the downstream region with 45%-Hct in the same microvessel. In the 20-μm microvessel with high-Hct condition (45%), the Pf-IRBCs slow down the velocity of the surrounding HRBCs and then locally elevate the volume fraction and result in the accumulating of the RBCs at the center of the vessels. Moreover, the Pf-IRBCs have a tendency to migrate to the edge of the RBC aggregates, which is called margination of red blood cells. This study is of some significance to the development of biomechanical experiments and devices.

Investigation of microvascular morphological measures for skeletal muscle tissue oxygenation by image-based modelling in three dimensions.

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, especially for skeletal muscle during exercise. Traditionally, microvascular oxygen supply capability is assessed by the analysis of morphological measures on transverse cross-sections of muscle, e.g. capillary density or capillary-to-fibre ratio. In this work, we investigate the relationship between microvascular structure and muscle tissue oxygenation in mice. Phase contrast imaging was performed using synchrotron radiation computed tomography (SR CT) to visualize red blood cells (RBCs) within the microvasculature in mouse soleus muscle. Image-based mathematical modelling of the oxygen diffusion from the RBCs into the muscle tissue was subsequently performed, as well as a morphometric analysis of the microvasculature. The mean tissue oxygenation was then compared with the morphological measures of the microvasculature. RBC volume fraction and spacing (mean distance of any point in tissue to the closest RBC) emerged as the best predictors for muscle tissue oxygenation, followed by length density (summed RBC length over muscle volume). The two-dimensional measures of capillary density and capillary-to-fibre ratio ranked last. We, therefore, conclude that, in order to assess the states of health of muscle tissue, it is advisable to rely on three-dimensional morphological measures rather than on the traditional two-dimensional measures.

MAGNETOHYDRODYNAMIC EFFECTS ON THE GRANULAR TEMPERATURE OF RED BLOOD CELLS IN MICROVASCULATURE

The migration of Red Blood Cells (RBCs) from the wall towards the center of a narrow vessel is the result of the Fahraeus–Lindqvist effect which contemplates the dependence of viscosity and diameter. The kinetic theory explains the formation of the near-wall cell-depleted layer introducing the granular temperature that is defined as the mean square of RBCs fluctuations. The proposed mathematical model elucidates the effect of an externally applied magnetic field on the velocity and granular temperature of RBCs in a microvasculature. The effect of the volume fraction of RBCs on the velocity and granular temperature profiles is also presented and discussed. Based on the insight of the kinetic theory, the application of a stronger static magnetic field probably leads to a restriction of the migration process of RBCs towards the center of the microvessel.

High-Throughput and Label-Free Blood-on-a-Chip for Malaria Diagnosis.

The malaria parasite Plasmodium falciparum (Pf) changes the structure and mechanical properties of red blood cells (RBCs). These changes decrease deformability and increase cytoadherence of Pf-infected RBCs to the vascular endothelium, eventually leading to flow occlusions in capillary vessels. In this study, to detect Pf-infected RBCs effectively, deformability and viscosity of blood sample are measured simultaneously and indirectly by quantifying blood flow in a microfluidic device. The microfluidic device is designed by mimicking a Wheatstone-bridge electric circuit. To measure RBC deformability, a deformability assessment chamber (DAC) at the left lower side channel has parallel microfluidic filters. After delivering blood sample and 1× PBS solution at the same flow rate, hemodynamic properties are measured using a time-resolved microparticle image velocimetry technique. Blood volume delivered into the DAC for 200 s is evaluated as a deformability index. Subsequently, blood viscosity is quantified by monitoring blood-filled width of parallel flows in the microfluidic device. The proposed method is applied to evaluate variations in biophysical properties of blood samples partially mixed with normal RBCs and hardened RBCs. As a result, RBC deformability is more effective than blood viscosity in the detection of blood samples with hardened RBC volume fraction of 5%. The microfluidic device is also applied to detect Pf-infected RBCs. When parasitemia is greater than 0.515% for ring stage, 0.0544% for trophozoite stage, and 0.0054% for schizont stage, the measured velocity fields show unstable behavior because of cytoadherence of Pf-infected RBCs. Blood volume delivered into the DAC significantly decreases with increasing parasitemia. The experimental method proposed in this study can detect Pf-infected RBCs with good accuracy.

Blood linear viscoelasticity by small amplitude oscillatory flow

Blood is a complex fluid with non-Newtonian characteristics and consists primarily of a concentrated suspension of red blood cells (RBCs) characterized by high deformability and aggregability. The majority of both research and clinical investigations on blood rheology is based on steady shear measurements aimed at determining blood viscosity as a function of shear rate. On the other hand, investigations of blood rheology in the linear viscoelastic regime are sparse in the literature and currently limited. In principle, small amplitude oscillatory flow is best suited to study blood microstructure and rheology under quasi-static conditions, which are relevant in a range of applications, from blood storage to blood aggregability testing. Here, we present the first systematic experimental investigation of blood rheological behavior in the linear viscoelastic regime, by performing oscillatory shear measurements by conventional bulk rheology. The storage (G′) and loss (G″) moduli of whole human blood have been measured over an extended range of frequencies [0.1–30 rad/s]. Data show that G″ predominates over G′ across the entire tested range of frequency. By comparing steady and oscillatory shear viscosity, it was found that the Cox-Merz rule is followed to a good approximation, with higher deviations at small shear rate/frequencies. The effects of RBC volume fraction and of aggregating media (i.e., dextran solution at two different concentrations) have been also investigated. Overall, our results are consistent with the behavior of a weakly attractive suspension, where RBCs form reversible aggregates that can be broken by the action of flow.

Breakdown of deterministic lateral displacement efficiency for non-dilute suspensions: A numerical study

We investigate the effect of particle volume fraction on the efficiency of deterministic lateral displacement (DLD) devices. DLD is a popular passive sorting technique for microfluidic applications. Yet, it has been designed for treating dilute suspensions, and its efficiency for denser samples is not well known. We perform 3D simulations based on the immersed-boundary, lattice-Boltzmann and finite-element methods to model the flow of red blood cells (RBCs) in different DLD devices. We quantify the DLD efficiency in terms of appropriate “failure” probabilities and RBC counts in designated device outlets. Our main result is that the displacement mode breaks down upon an increase of RBC volume fraction, while the zigzag mode remains relatively robust. This suggests that the separation of larger particles (such as white blood cells) from a dense RBC background is simpler than separating smaller particles (such as platelets) from the same background. The observed breakdown stems from non-deterministic particle collisions interfering with the designed deterministic nature of DLD devices. Therefore, we postulate that dense suspension effects generally hamper efficient particle separation in devices based on deterministic principles.

Effects of aortic irregularities on blood flow

Anatomic aortic anomalies are seen in many medical conditions and are known to cause disturbances in blood flow. Turner syndrome (TS) is a genetic disorder occurring only in females where cardiovascular anomalies, particularly of the aorta, are frequently encountered. In this study, numerical simulations are applied to investigate the flow characteristics in four TS patient- related aortic arches (a normal geometry, dilatation, coarctation and elongation of the transverse aorta). The Quemada viscosity model was applied to account for the non-Newtonian behavior of blood. The blood is treated as a mixture consisting of water and red blood cells (RBC) where the RBCs are modeled as a convected scalar. The results show clear geometry effects where the flow structures and RBC distribution are significantly different between the aortas. Transitional flow is observed as a jet is formed due to a constriction in the descending aorta for the coarctation case. RBC dilution is found to vary between the aortas, influencing the WSS. Moreover, the local variations in RBC volume fraction may induce large viscosity variations, stressing the importance of accounting for the non-Newtonian effects.

Synergy between shear-induced migration and secondary flows on red blood cells transport in arteries: considerations on oxygen transport.

Shear-induced migration of red blood cells (RBCs) is a well-known phenomenon characterizing blood flow in the small vessels (micrometre to millimetre size) of the cardiovascular system. In large vessels, like the abdominal aorta and the carotid artery (millimetre to centimetre size), the extent of this migration and its interaction with secondary flows has not been fully elucidated. RBC migration exerts its influence primarily on platelet concentration, oxygen transport and oxygen availability at the luminal surface, which could influence vessel wall disease processes in and adjacent to the intima. Phillips' shear-induced particle migration model, coupled to the Quemada viscosity model, was employed to simulate the macroscopic behaviour of RBCs in four patient-specific geometries: a normal abdominal aorta, an abdominal aortic aneurysm (AAA), a normal carotid bifurcation and a stenotic carotid bifurcation. Simulations show a migration of RBCs from the near-wall region with a lowering of wall haematocrit (volume fraction of RBCs) on the posterior side of the normal aorta and on the lateral-external side of the iliac arteries. A marked migration is observed on the outer wall of the carotid sinus, along the common carotid artery and in the carotid stenosis. No significant migration is observed in the AAA. The spatial and temporal patterns of wall haematocrit are correlated with the near-wall shear layer and with the secondary flows induced by the vessel curvature. In particular, secondary flows accentuate the initial lowering in RBC near-wall concentration by convecting RBCs from the inner curvature side to the outer curvature side. The results reinforce data in literature showing a decrease in oxygen partial pressure on the inner curvature wall of the carotid sinus induced by the presence of secondary flows. The lowering of wall haematocrit is postulated to induce a decrease in oxygen availability at the luminal surface through a diminished concentration of oxyhaemoglobin, hence contributing, with the reported lowered oxygen partial pressure, to local hypoxia.

Modeling of the blood rheology in steady-state shear flows

We undertake here a systematic study of the rheology of blood in steady-state shear flows. As blood is a complex fluid, the first question that we try to answer is whether, even in steady-state shear flows, we can model it as a rheologically simple fluid, i.e., we can describe its behavior through a constitutive model that involves only local kinematic quantities. Having answered that question positively, we then probe as to which non-Newtonian model best fits available shear stress vs shear-rate literature data. We show that under physiological conditions blood is typically viscoplastic, i.e., it exhibits a yield stress that acts as a minimum threshold for flow. We further show that the Casson model emerges naturally as the best approximation, at least for low and moderate shear-rates. We then develop systematically a parametric dependence of the rheological parameters entering the Casson model on key physiological quantities, such as the red blood cell volume fraction (hematocrit). For the yield stress, we base our description on its critical, percolation-originated nature. Thus, we first determine onset conditions, i.e., the critical threshold value that the hematocrit has to have in order for yield stress to appear. It is shown that this is a function of the concentration of a key red blood cell binding protein, fibrinogen. Then, we establish a parametric dependence as a function of the fibrinogen and the square of the difference of the hematocrit from its critical onset value. Similarly, we provide an expression for the Casson viscosity, in terms of the hematocrit and the temperature. A successful validation of the proposed formula is performed against additional experimental literature data. The proposed expression is anticipated to be useful not only for steady-state blood flow modeling but also as providing the starting point for transient shear, or more general flow modeling.

Hematocrit and flow rate regulate the adhesion of platelets to von Willebrand factor

Primary hemostasis and blood clotting is known to be influenced by the red blood cell volume fraction (hematocrit) in blood. Depressed or elevated levels of red blood cells can lead to vascular perfusion problems ranging from bleeding to thrombus formation. The early stage of hemostasis and thus blood clotting in all vessel sections from the arterial to the venous system involves the adhesion of platelets to von Willebrand factor. Here we present experimental and theoretical results showing that the adhesion probability of platelets to von Willebrand factor is strongly and nonlinearly dependent on hematocrit and flow rate. Interestingly, the actual binding forces are not markedly different, which suggest that the origin of such behavior is in the distribution of platelets. Using hydrodynamic simulations of a simple model, we explicitly show that the higher the hematocrit and the flow rate, the larger the amount of platelets residing close to the wall. Our simulation results, which are in excellent agreement with the experimental observations, explain why such phenomena occur. We believe that the nonhomogeneous red blood cell distribution as well as the shear dependent hydrodynamic interaction is key for the accumulation of platelets on the vessel wall. The work we present here is an important step forward from our earlier work on single molecules and extends into the collective cellular behavior of whole blood. It sheds new light on the correlation between hematocrit and the initial steps in hemostasis and thrombosis, and outlines advances for the treatment of vascular diseases associated with high levels of red blood cells. These results are not only highly relevant for the field of hemostasis and the physics of blood clotting but are also of powerful impact in applied science most obviously in drug delivery and colloidal science.

Membrane tension of red blood cells pairwisely interacting in simple shear flow

Flow-induced membrane tension contributes to the release of molecules by red blood cells (RBCs), and extremely high tension may cause haemolysis. Here, we investigated the membrane tension of RBCs during pairwise interactions in simple shear flow, given that pairwise interactions form the basis of many-body interactions. RBCs were modelled as capsules with a two-dimensional hyperelastic membrane, and large deformations were solved by the finite element method. Due to the small size of the RBCs, surrounding fluid motion was estimated as a Stokes flow and solved by the boundary element method. The results showed that the maximum isotropic tension appeared around the dimple of the biconcave surface and not around the rim. A comparison of the results with solitary cases indicated that the maximum principal tension and isotropic tension were significantly increased by cell–cell interaction effects. As the volume fraction of RBCs is large under physiological conditions, as well as in blood flow in vitro, cell–cell interactions must be analysed carefully when considering mechanotransduction and haemolysis in blood flow.

Ordering and arrangement of deformed red blood cells in flow through microcapillaries

The shapes and alignment of elastic vesicles similar to red blood cells (RBCs) in cylindrical capillary flow are investigated by mesoscopic hydrodynamic simulations. We study the collective flow behavior of many RBCs, where the capillary diameter is comparable to the diameter of the RBCs. Two essential control parameters are the RBC volume fraction (the tube hematocrit, HT), and the suspension flow velocity. Depending on HT, flow velocity and capillary radius, the RBC suspension exhibits a disordered phase and two distinct ordered phases, consisting of a single file of parachute-shaped cells and a zigzag arrangement of slipper-shaped cells, respectively. We argue that thermal fluctuations, included in the simulation method, coupled to hydrodynamic flows are important contributors to the RBC morphology. We examine the changes to the phase structures when the capillary diameter and the material properties (bending rigidity κ and stretching modulus μ) of the model RBCs are varied, constructing phase diagrams for each case. We focus on capillary diameters, which range from about 1.0 to about 1.4 times the RBC long diameter. For the smallest capillary diameter, the single-file arrangement dominates; for the largest diameter, the ordered zigzag arrangement begins to loose its stability and alternates with an asymmetric structure with two lanes of differently oriented cells. In simulations with long capillaries, the coexistence of different phases can be observed.

Estimation of red blood cell volume fraction from overall permittivity measurements

The rapid testing of red blood cell (RBC) volume fraction (“hematocrit”) is becoming increasingly important to identify blood disorders (“hemoglobinopathies”). Electromagnetic techniques provide an advantageous way to measure blood properties, primarily because they are inexpensive, quick and noninvasive. The goal of this paper is to develop estimates of the RBC volume fraction levels of whole blood from macroscopic electromagnetic (permittivity) measurements. The approach taken is to generate volume fraction estimates by inverting classical bounds on the effective permittivity of dielectric mixtures. The usefulness of the approach is that, given the permittivities of the plasma (known), cells (known) and whole mixture (measured), one can determine the cell volume fraction and compare it to the levels found in healthy blood. The deviation of the properties can be used to help characterize certain blood disorders. The expressions developed are not limited to RBC measurement, and are applicable to any cell-in-solution system. Through correlation of our laboratory measurements, the analytical expressions and direct large-scale numerical simulations, the results suggest that RBCs form high-permittivity cell-networks by making cell-to-cell contact, even at relatively low volume fraction.