erythrocyte-sedimentation-rate-physics-driven-characterization

Erythrocyte Sedimentation Rate: A Physics-Driven Characterization in a Medical Context

Erythrocyte (or red blood cell) sedimentation rate (ESR) is a physical derived parameter of blood which is often used in routine health checks and medical ...

Saarland University

We present experiments on RBCs that flow through micro-capillaries under physiological conditions. The strong flow-shape coupling of these deformable objects leads to a rich variety of cluster formation. We show that the RBC clusters form as a subtle imbrication between hydrodynamic interactions and adhesion forces because of plasma proteins, mimicked by the polymer dextran. Clusters form along the capillaries and macromolecule-induced adhesion contributes to their stability. However, at high yet physiological flow velocities, shear stresses overcome part of the adhesion forces, and cluster stabilization due to hydrodynamics becomes stronger. For the case of pure hydrodynamic interaction, cell-to-cell distances have a pronounced bimodal distribution. Our 2D-numerical simulations on vesicles capture the transition between adhesive and non-adhesive clusters at different flow velocities.

Clusters of red blood cells in microcapillary flow: hydrodynamic versus macromolecule induced interaction.

In this study we have applied a model to explain the reported subdiffusion of particles in mucus, based on the measured mean squared displacements (MSD). The model considers Brownian diffusion of particles in a confined geometry, made from permeable membranes. The applied model predicts a normal diffusive behavior at very short and long time lags, as observed in several experiments. In between these timescales, we find that the "subdiffusive" regime is only a transient effect, MSD∝τ,α<1. The only parameters in the model are the diffusion-coefficients at the limits of very short and long times, and the distance between the permeable membranes L. Our numerical results are in agreement with published experimental data for realistic assumptions of these parameters. Finally, we show that only particles with a diameter less than 40 nm are able to pass through a mucus layer by passive Brownian motion.

A Model for the Transient Subdiffusive Behavior of Particles in Mucus.

Peritrichous bacteria synchronize and bundle their flagella to actively swim, while disruption of the bundle leads to a slow motility phase with a weak propulsion. It is still not known whether the number of flagella represents an evolutionary adaptation toward optimizing bacterial navigation. We study the swimming dynamics of differentially flagellated  strains in a quasi-two-dimensional system. We find that decreasing the number of flagella   reduces the average turning angle between two successive run phases and enhances the run time and the directional persistence of the run phase. As a result, having fewer flagella is beneficial for long-distance transport and fast spreading, while having a lot of flagella is advantageous for the processes that require a slower spreading, such as biofilm formation. We develop a two-state random walk model that incorporates spontaneous switchings between the states and yields exact analytical expressions for transport properties, in remarkable agreement with experiments. The results of numerical simulations based on our two-state model suggest that the efficiency of searching and exploring the environment is optimized at intermediate values of  . The optimal choice of  , for which the search time is minimized, decreases with increasing the size of the environment in which the bacteria swim.

Flagellar number governs bacterial spreading and transport efficiency.

Constrictions in blood vessels and microfluidic devices can dramatically change the spatial distribution of passing cells or particles and are commonly used in biomedical cell sorting applications. However, the three-dimensional nature of cell focusing in the channel cross-section remains poorly investigated. Here, we explore the cross-sectional distribution of living and rigid red blood cells passing a constricted microfluidic channel by tracking individual cells in multiple layers across the channel depth and across the channel width. While cells are homogeneously distributed in the channel cross-section pre-contraction, we observe a strong geometry-induced focusing towards the four channel faces post-contraction. The magnitude of this cross-sectional focusing effect increases with increasing Reynolds number for both living and rigid red blood cells. We discuss how this non-uniform cell distribution downstream of the contraction results in an apparent double-peaked velocity profile in particle image velocimetry analysis and show that trapping of red blood cells in the recirculation zones of the abrupt construction depends on cell deformability.

Cross-sectional focusing of red blood cells in a constricted microfluidic channel.

Correction for 'Cross-sectional focusing of red blood cells in a constricted microfluidic channel' by Asena Abay et al., Soft Matter, 2020, 16, 534-543.

Correction: Cross-sectional focusing of red blood cells in a constricted microfluidic channel.

The microvascular networks in the body of vertebrates consist of the smallest vessels such as arterioles, capillaries, and venules. The flow of red blood cells (RBCs) through these networks ensures the gas exchange in as well as the transport of nutrients to the tissues. Any alterations in this blood flow may have severe implications on the health state. Because the vessels in these networks obey dimensions similar to the diameter of RBCs, dynamic effects on the cellular scale play a key role. The steady progression in the numerical modeling of RBCs, even in complex networks, has led to novel findings in the field of hemodynamics, especially concerning the impact and the dynamics of lingering events when a cell meets a branch of the network. However, these results are yet to be matched by a detailed analysis of the lingering experiments in vivo. To quantify this lingering effect in in vivo experiments, this study analyzes branching vessels in the microvasculature of Syrian golden hamsters via intravital microscopy and the use of an implanted dorsal skinfold chamber. It also presents a detailed analysis of these lingering effects of cells at the apex of bifurcating vessels, affecting the temporal distribution of plasmatic zones of blood flow in the branches and even causing a partial blockage in severe cases.

Lingering Dynamics in Microvascular Blood Flow.

Knowledge about the flow field of the plasma around the red blood cells in capillary flow is important for a physical understanding of blood flow and the transport of micro- and nanoparticles and molecules in the flowing plasma. We conducted an experimental study on the flow field around red blood cells in capillary flow that is complemented by simulations of vortical flow between red blood cells.

Vortical flow structures induced by red blood cells in capillaries.

(1) Background: Chorea-acanthocytosis and McLeod syndrome are the core diseases among the group of rare neurodegenerative disorders called neuroacanthocytosis syndromes (NASs). NAS patients have a variable number of irregularly spiky erythrocytes, so-called acanthocytes. Their detection is a crucial but error-prone parameter in the diagnosis of NASs, often leading to misdiagnoses. (2) Methods: We measured the standard Westergren erythrocyte sedimentation rate (ESR) of various blood samples from NAS patients and healthy controls. Furthermore, we manipulated the ESR by swapping the erythrocytes and plasma of different individuals, as well as replacing plasma with dextran. These measurements were complemented by clinical laboratory data and single-cell adhesion force measurements. Additionally, we followed theoretical modeling approaches. (3) Results: We show that the acanthocyte sedimentation rate (ASR) with a two-hour read-out is significantly prolonged in chorea-acanthocytosis and McLeod syndrome without overlap compared to the ESR of the controls. Mechanistically, through modern colloidal physics, we show that acanthocyte aggregation and plasma fibrinogen levels slow down the sedimentation. Moreover, the inverse of ASR correlates with the number of acanthocytes (R2=0.61, p=0.004). (4) Conclusions: The ASR/ESR is a clear, robust and easily obtainable diagnostic marker. Independently of NASs, we also regard this study as a hallmark of the physical view of erythrocyte sedimentation by describing anticoagulated blood in stasis as a percolating gel, allowing the application of colloidal physics theory.

Acanthocyte Sedimentation Rate as a Diagnostic Biomarker for Neuroacanthocytosis Syndromes: Experimental Evidence and Physical Justification.

Unsteady and pulsatile flows receive increasing attention due to their potential to enhance various microscale processes. Further, they possess significant relevance for microfluidic studies under physiological flow conditions. However, generating a precise time-dependent flow field with commercial, pneumatically operated pressure controllers remains challenging and can lead to significant deviations from the desired waveform. In this study, we present a method to correct such deviations and thus optimize pulsatile flows in microfluidic experiments using two commercial pressure pumps. Therefore, we first analyze the linear response of the systems to a sinusoidal pressure input, which allows us to predict the time-dependent pressure output for arbitrary pulsatile input signals. Second, we explain how to derive an adapted input signal, which significantly reduces deviations between the desired and actual output pressure signals of various waveforms. We demonstrate that this adapted pressure input leads to an enhancement of the time-dependent flow of red blood cells in microchannels. The presented method does not rely on any hardware modifications and can be easily implemented in standard pressure-driven microfluidic setups to generate accurate pulsatile flows with arbitrary waveforms.

Optimizing pressure-driven pulsatile flows in microfluidic devices.

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.

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

The erythrocyte sedimentation rate (ESR) is one of the oldest medical diagnostic tools. However, currently there is some debate on the structure formed by the cells during the sedimentation process. While the conventional view is that erythrocytes sediment as separate aggregates, others have suggested that they form a percolating gel, similar to other colloidal suspensions. However, visualization of aggregated erythrocytes, which would settle the question, has always been challenging. Direct methods usually study erythrocytes in 2D situations or low hematocrit (∼1%). Indirect methods, such as scattering or electric measurements, provide insight on the suspension evolution, but cannot directly discriminate between open or percolating structures. Here, we achieved a direct probing of the structures formed by erythrocytes in blood at stasis. We focused on blood samples at rest with controlled hematocrit of 45%, from healthy donors, and report observations from three different optical imaging techniques: direct light transmission through thin samples, two-photon microscopy and light-sheet microscopy. The three techniques, used in geometries with thickness from 150 μm to 3 mm, highlight that erythrocytes form a continuous network with characteristic cracks, i.e., a colloidal gel. The characteristic distance between the main cracks is of the order of ∼100 μm. A complete description of the structure then requires a field of view of the order of ∼1 mm, in order to obtain a statistically relevant number of structural elements. A quantitative analysis of the erythrocyte related processes and interactions during the sedimentation need a further refinement of the experimental set-ups.

Imaging Erythrocyte Sedimentation in Whole Blood.

The erythrocyte sedimentation rate is one of the oldest medical diagnostic methods whose physical mechanisms remain debatable today. Using both light microscopy and mesoscale cell-level simulations, we show that erythrocytes form a soft-particle gel. Furthermore, the high volume fraction of erythrocytes, their deformability, and weak attraction lead to unusual properties of this gel. A theoretical model for the gravitational collapse is developed, whose predictions are in agreement with detailed macroscopic measurements of the interface velocity.

Erythrocyte Sedimentation: Collapse of a High-Volume-Fraction Soft-Particle Gel.

The erythrocyte (or red blood cell) sedimentation rate (ESR) is commonly interpreted as a measure of cell aggregation and as a biomarker of inflammation. It is well known that an increase of fibrinogen concentration, an aggregation-inducing protein for erythrocytes, leads to an increase of the sedimentation rate of erythrocytes, which is generally explained through the formation and faster settling of large disjoint aggregates. However, many aspects of erythrocyte sedimentation conform well with the collapse of a particle gel rather than with the sedimentation of disjoint aggregates. Using experiments and cell-level numerical simulations, we systematically investigate the dependence of ESR on fibrinogen concentration and its relation to the microstructure of the gel-like erythrocyte suspension. We show that for physiological aggregation interactions, an increase in the attraction strength between cells results in a cell network with larger void spaces. This geometrical change in the network structure occurs due to anisotropic shape and deformability of erythrocytes and leads to an increased gel permeability and faster sedimentation. Our results provide a comprehensive relation between the ESR and the cell-level structure of erythrocyte suspensions and support the gel hypothesis in the interpretation of blood sedimentation.

Erythrocyte sedimentation: Effect of aggregation energy on gel structure during collapse.

(1) Background: When red blood cells are centrifuged in a continuous Percoll-based density gradient, they form discrete bands. While this is a popular approach for red blood cell age separation, the mechanisms involved in banding were unknown. (2) Methods: Percoll centrifugations of red blood cells were performed under various experimental conditions and the resulting distributions analyzed. The age of the red blood cells was measured by determining the protein band 4.1a to 4.1b ratio based on western blots. Red blood cell aggregates, so-called , were monitored microscopically. A mathematical model for the centrifugation process was developed. (3) Results: The red blood cell band pattern is reproducible but re-centrifugation of sub-bands reveals a new set of bands. This is caused by red blood cell aggregation. Based on the aggregation, our mathematical model predicts the band formation. Suppression of red blood cell aggregation reduces the band formation. (4) Conclusions: The red blood cell band formation in continuous Percoll density gradients could be explained physically by red blood cell aggregate formation. This aggregate formation distorts the density-based red blood cell age separation. Suppressing aggregation by osmotic swelling has a more severe effect on compromising the RBC age separation to a higher degree.

Continuous Percoll Gradient Centrifugation of Erythrocytes-Explanation of Cellular Bands and Compromised Age Separation.

The analysis of nanoparticle (NP) dynamics in live cell studies by video tracking provides detailed information on their interactions and trafficking in the cells. Although the video analysis is not yet routinely used in NP studies, the equipment suitable for the experiments is already available in most laboratories. Here, we compare trajectory patterns, diffusion coefficients, and particle velocities of NPs in A549 cells with a rather simple experimental setup consisting of a fluorescence microscope and openly available trajectory analysis software. The studied NPs include commercial fluorescent polymeric particles and two subpopulations of PC-3 cell-derived extracellular vesicles (EVs). As bioderived natural nanoparticles, the fluorescence intensities of the EVs limited the recording speed. Therefore, we studied the effect of the recording frame rate and analysis parameters to the trajectory results with bright fluorescent commercial NPs. We show that the trajectory classification and the apparent particle velocities are affected by the recording frame rate, while the diffusion constants stay comparable. The NP trajectory patterns were similar for all NP types and resembled intracellular vesicular transport. Interestingly, the EV movements were faster than the commercial NPs, which contrasts with their physical sizes and may indicate a greater role of the motor proteins in their intracellular transports.

Intracellular Dynamics of Extracellular Vesicles by Segmented Trajectory Analysis.

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 is 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 works. 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).

Article	Year
Clusters of red blood cells in microcapillary flow: hydrodynamic versus macromolecule induced interaction. Soft matter\| PubMed ID: 27714335	2016
A Model for the Transient Subdiffusive Behavior of Particles in Mucus. Biophysical journal\| PubMed ID: 28076809	2017
Flagellar number governs bacterial spreading and transport efficiency. Science advances\| PubMed ID: 30263953	2018
Cross-sectional focusing of red blood cells in a constricted microfluidic channel. Soft matter\| PubMed ID: 31808773	2020
Correction: Cross-sectional focusing of red blood cells in a constricted microfluidic channel. Soft matter\| PubMed ID: 32039425	2020
Lingering Dynamics in Microvascular Blood Flow. Biophysical journal\| PubMed ID: 33359171	2021
Vortical flow structures induced by red blood cells in capillaries. Microcirculation (New York, N.Y. : 1994)\| PubMed ID: 33666310	2021
Acanthocyte Sedimentation Rate as a Diagnostic Biomarker for Neuroacanthocytosis Syndromes: Experimental Evidence and Physical Justification. Cells\| PubMed ID: 33918219	2021
Optimizing pressure-driven pulsatile flows in microfluidic devices. Lab on a chip\| PubMed ID: 34008605	2021
Red blood cell shape transitions and dynamics in time-dependent capillary flows. Biophysical journal\| PubMed ID: 34896369	2022
Imaging Erythrocyte Sedimentation in Whole Blood. Frontiers in physiology\| PubMed ID: 35153805	2021
Erythrocyte Sedimentation: Collapse of a High-Volume-Fraction Soft-Particle Gel. Physical review letters\| PubMed ID: 35275655	2022
Erythrocyte sedimentation: Effect of aggregation energy on gel structure during collapse. Physical review. E\| PubMed ID: 35291110	2022
Continuous Percoll Gradient Centrifugation of Erythrocytes-Explanation of Cellular Bands and Compromised Age Separation. Cells\| PubMed ID: 35455975	2022
Intracellular Dynamics of Extracellular Vesicles by Segmented Trajectory Analysis. Analytical chemistry\| PubMed ID: 36512439	2022
Red blood cell lingering modulates hematocrit distribution in the microcirculation. Biophysical journal\| PubMed ID: 36932676	2023

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