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

Anil Kumar Dasanna, Alexis Darras, Thomas John, Gerhard Gompper, Lars Kaestner, Christian Wagner, and Dmitry A. Fedosov

Phys. Rev. E 105, 024610 – Published 23 February 2022

Abstract

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.

Received 23 July 2021
Accepted 2 February 2022

DOI:https://doi.org/10.1103/PhysRevE.105.024610

Physics Subject Headings (PhySH)

Cell aggregation Collective behavior Flows in porous media Multiphase flows

Blood plasma Colloidal gel Red blood cells

Coarse graining Master equation Optical techniques

Physics of Living SystemsPolymers & Soft MatterFluid Dynamics

Authors & Affiliations

Anil Kumar Dasanna ¹, Alexis Darras ^2,*, Thomas John ², Gerhard Gompper ¹, Lars Kaestner ^2,3, Christian Wagner ^2,4, and Dmitry A. Fedosov ¹

¹Theoretical Physics of Living Matter, Institute of Biological Information Processing and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
²Experimental Physics, Saarland University, 66123 Saarbruecken, Germany
³Theoretical Medicine and Biosciences, Saarland University, 66424 Homburg, Germany
⁴Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg

^*alexis.charles.darras@gmail.com

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

Alexis Darras, Anil Kumar Dasanna, Thomas John, Gerhard Gompper, Lars Kaestner, Dmitry A. Fedosov, and Christian Wagner

Phys. Rev. Lett. 128, 088101 (2022)

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Vol. 105, Iss. 2 — February 2022

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Images

Figure 1
ESR experiments. Cuvettes containing blood samples with various levels of fibrinogen are shown after 2 hours at rest. Hematocrit (i.e., erythrocyte volume fraction) in all containers has been adjusted to $ϕ = 0.45$ . The very left container corresponds to erythrocytes suspended in autologous serum (no fibrinogen), while the very right contains erythrocytes in autologous blood plasma (maximum amount of fibrinogen). Middle containers contain cells suspended in a mixture of serum and plasma, with volume proportions of $25 %, 50 %$ , and $75 %$ of plasma, from left to right. The various height characteristics $(h_{0}, h (t)$ and $Δ h (t))$ are also indicated.
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Figure 2
(a) Time dependence of height of the interface between dense erythrocyte suspension and cell-free plasma, for various fibrinogen concentrations. The curves show the relative variation $Δ h / h_{0} = [h_{0} - h (t)] / h_{0}$ which corresponds to the height of the cell-free plasma layer. The symbols are experimental data, while the curves are fits from the theoretical model for $h (t)$ in Eq. (2). (b) Associated interface speed as a function of the volume fraction $ϕ (t) = ϕ_{0} h_{0} / h (t)$ . The symbol data are computed from a smoothing spline of the $Δ h$ measurements, while the curves correspond to the expected speed from the fit parameters in Eq. (1).
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Figure 3
Dependence of the model parameters on the fibrinogen concentration for different blood donors. Different symbols and colors indicate different donors. (a) Initial sedimentation velocity at $t_{0}$ computed using Eq. (1) with $ϕ = ϕ_{0} = 0.45$ . (b) Dimensionless characteristic time $γ$ of the sedimentation process. (c) The final volume fraction $ϕ_{m}$ . (d) The delay time $t_{0}$ before the sedimentation starts.
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Figure 4
Pictures of 2D cell networks obtained for various fibrinogen concentrations in PBS, after sedimentation to the bottom of a microscopy chamber. The final hematocrit at the bottom of the chamber within a $8 µm$ height monolayer of erythrocytes is equal to approximately $ϕ = 0.56$ . Qualitative differences in aggregate geometries and characteristic sizes of the pores are clearly visible for different fibrinogen concentrations. Insets in (a) and (c) are schemes of the $x z$ plane in the quasi-2D experiments, for both minimal (a) and maximal (c) fibrinogen concentration. Although the volume fraction is the same for each measurement, the total 2D pore area in the $x y$ plane increases from (a) to (c) because more cells are seen from the side when incorporated in a rouleau, while most of the cells lie flat at the bottom of the container in (a).
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Figure 5
Mean pore sizes within a quasi-2D percolating network of erythrocytes at the bottom of the observation chamber as a function of fibrinogen concentration in PBS. A trend of increasing pore size with increasing fibrinogen concentration is observed at fibrinogen concentrations above 300 mg/dl. The bars represent standard deviations of the average values measured in various samples from different donors.
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Figure 6
Effect of interaction strength on the structure and permeability of erythrocyte aggregates from simulations. (a–c) Gelation process from hydrodynamic simulations for different interaction strengths $ε = {0, 2.5, 4.4} k_{B} T$ . All snapshots are for volume fraction $ϕ = 0.35$ and show a $10 − μ m$ -thick layer in $z$ with a cross section of $50 μ m \times 50 μ m$ in $x − y$ . (d) Permeability coefficient, computed as $k = (1 - ϕ) v η / \frac{\partial P}{\partial z}$ , as a function of the interaction strength $ε$ . The data are displayed for two different hematocrits, and the lines are a guide to the eye. (e) The average pore size $〈 l 〉$ from simulations for varying interaction strength $ε$ . Errors on the average are typically smaller than the symbol sizes. The corresponding distributions of pore sizes are shown in Supplemental Fig. 5 [58]. The lines are a guide to the eye. (f) Permeability coefficient $k$ as a function of the mean pore size $l$ obtained by varying the interaction strength. The lines are quadratic fits ( $k = A + B {〈 l 〉}^{2}$ with $A$ and $B$ being fit parameters), which follow the scaling in the Carman-Kozeny relationship ( $k \propto a^{2}$ ). Except for the data points marked by upward triangles, all data were generated with $ϕ = 0.25$ . (g) The average pore size $〈 l 〉$ for different suspension conditions, including a static (no flow) case with deformable RBCs and a suspension of rigid RBCs and spherical particles. All curves are for a volume fraction of $ϕ = 0.25$ . The lines are a guide to the eye. Errors on the average are smaller than the symbol sizes.
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