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 – Published 23 February 2022

Abstract

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.

Received 23 July 2021
Accepted 21 January 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.088101

Physics Subject Headings (PhySH)

Cell aggregation Collective behavior Complex fluids Flows in porous media Medical physics & public health Multiphase flows

Blood Blood plasma Colloidal gel Red blood cells

Polymers & Soft MatterPhysics of Living SystemsFluid Dynamics

Authors & Affiliations

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

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

^*Corresponding author. alexis.charles.darras@gmail.com

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 (2022)

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Vol. 128, Iss. 8 — 25 February 2022

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Images

Figure 1
Possible regimes of erythrocyte sedimentation. (a) Experimental photograph of a low volume fraction ( $ϕ_{0} = 0.2$ ) erythrocyte suspension, after 20 min at rest in a cuvette with quadratic cross section. A diffuse interface hints to a sedimentation of separate aggregates. (b) Snapshot from simulation: well-dispersed suspension of erythrocytes for $ϕ = 0.25$ and no attraction force between the cells. (c) Snapshot from simulation: formation of rouleaux structures at $ϕ = 0.25$ and physiological attraction between the cells ( $ε = 2.5 k_{B} T$ , see the companion paper for details [18]). (d) False-color photograph of erythrocytes clusters in a $150 μ m$ thick container, at volume fraction $ϕ = 0.20$ (see also Supplemental Movie S1 [42]). (e) Percolation probability $p_{ϕ}$ is plotted against hematocrit $ϕ$ (simulations have a constant hematocrit due to periodic boundary conditions on $z$ ). The probability $p_{ϕ}$ is defined as the fraction of snapshots in which the largest cluster is percolating in both $x$ and $y$ (periodic) directions. The data are shown for both sedimentation and equilibrium. (f) A gel-like network for $ϕ = 0.4$ . All simulation snapshots have the same scale. (g) False-color photograph of the cracks for blood sedimentation in a $150 μ m$ thick container, at volume fraction $ϕ = 0.45$ (see also Supplemental Movie S2 [42]). (h) Erythrocyte suspension with physiological volume fraction ( $ϕ_{0} = 0.45$ ), after 2 hours at rest. A sharp interface, indicating a gel-like collapse behavior, is observed.
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Figure 2
Measurements of relative height reduction $Δ h / h_{0} = [h (0) - h (t)] / h (0)$ of the dense erythrocyte suspension below the free liquid phase (plasma), for various hematocrits. Note that $Δ h$ corresponds to the height of top plasma layer. The symbols are experimental data, while the curves are fits from our model for $h (t)$ from Eq. (5).
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Figure 3
Erythrocyte sedimentation for various initial volume fractions. (a) Measurements of velocity of the interface between the erythrocytes gel and the plasma (same experiments as in Fig. 2). The symbols are experimental data. The average velocity between two measurement points is $d h / d t$ , and $ϕ (t) = ϕ_{0} h_{0} / h (t)$ . The solid curve is obtained from Eq. (5) using average values of $γ = 0.42 \pm 0.06$ and $ϕ_{m} = 0.86 \pm 0.04$ from the entire set of measurements (16 samples from seven independent blood drawings). (b) Permeability coefficient from hydrodynamic simulations calculated as $k = (1 - ϕ) v η / (\partial P / \partial z)$ as a function of hematocrit. The assumed aggregation strength in simulations was $ε = 2.5 k_{B} T$ (see the companion paper [18]).
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