1
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Bedggood P, Ding Y, Metha A. Changes to the shape, orientation and packing of red cells as a function of retinal capillary size. BIOMEDICAL OPTICS EXPRESS 2024; 15:558-578. [PMID: 38404337 PMCID: PMC10890884 DOI: 10.1364/boe.511093] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/02/2023] [Revised: 12/13/2023] [Accepted: 12/18/2023] [Indexed: 02/27/2024]
Abstract
The free diameter of a red blood cell exceeds the lumen diameter of capillaries in the central nervous system, requiring significant deformation of cells. However the deformations undertaken in vivo are not well established due to the difficulty in observing cellular capillary flow in living human tissue. Here, we used high resolution adaptive optics imaging to non-invasively track 17,842 red blood cells in transit through 121 unique capillary segments of diameter 8 µm or less in the retina of 3 healthy human subjects. Within each vessel, a 2D en face profile was generated for the "average cell", whose shape was then inferred in 3D based on the key assumption of a circular capillary cross-section. From this we estimated the average volume, surface area, orientation, and separation between red cells within each capillary tube. Our results showed a network filtration effect, whereby narrower vessels were more likely to contain smaller cells (defined by surface area, which is thought not to vary during a cell's passage through the vascular system). A bivariate linear model showed that for larger cells in narrower vessels: cells re-orient themselves to align with the flow axis, their shape becomes more elongated, there are longer gaps between successive cells, and remarkably, that cell volume is less which implies the ejection of water from cells to facilitate capillary transit. Taken together, these findings suggest that red cells pass through retinal capillaries with some reluctance. A biphasic distribution for cell orientation and separation was evident, indicating a "tipping point" for vessels narrower than approx. 5 µm. This corresponds closely to the typical capillary lumen diameter, and may maximize sensitivity of cellular flow to small changes in diameter. We suggest that the minimization of unnecessary oxygen exchange, and hence of damage via reactive oxygen pathways, may have provided evolutionary pressure to ensure that capillary lumens are generally narrower than red blood cells.
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Affiliation(s)
- Phillip Bedggood
- Department of Optometry and Vision Sciences, The University of Melbourne, 3010, Australia
| | - Yifu Ding
- Department of Optometry and Vision Sciences, The University of Melbourne, 3010, Australia
| | - Andrew Metha
- Department of Optometry and Vision Sciences, The University of Melbourne, 3010, Australia
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2
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Gou Z, Zhang H, Nait-Ouhra A, Abbasi M, Farutin A, Misbah C. Dynamics and rheology of vesicles under confined Poiseuille flow. SOFT MATTER 2023; 19:9101-9114. [PMID: 37990752 DOI: 10.1039/d3sm01064c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2023]
Abstract
The rheological behavior and dynamics of a vesicle suspension, serving as a simplified model for red blood cells, are explored within a Poiseuille flow under the Stokes limit. Investigating vesicle response has led to the identification of novel solutions that complement previously documented forms like the parachute and slipper shapes. This study has brought to light the existence of alternative configurations, including a fully off-centered form and a multilobe structure. The study unveils the presence of two distinct branches associated with the slipper shape. One branch arises as a consequence of a supercritical bifurcation from the symmetric parachute shape, while the other emerges from a saddle-node bifurcation. Notably, the findings are represented through diagrams that display data collapsing harmoniously based on a combination of independent dimensionless parameters. Delving into the rheological implications, a remarkable observation emerges: the normalized viscosity (i.e. similar to intrinsic viscosity) exhibits a non-monotonic trend as a function of vesicle concentration. Initially, the normalized viscosity diminishes as the concentration increases, followed by a subsequent rise at higher concentrations. Noteworthy is the presence of a minimum value in the normalized viscosity at lower concentrations, aligning well with the concentrations observed in microcirculation scenarios. The intricate behavior of the normalized viscosity can be attributed to a delicate spatial arrangement within the suspension. Importantly, this trend echoes the observations made in a linear shear flow scenario, thereby underscoring the universality of the rheological behavior for confined suspensions.
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Affiliation(s)
- Zhe Gou
- College of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China
- Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France.
| | - Hengdi Zhang
- Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France.
| | - Abdessamad Nait-Ouhra
- Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France.
- Laboratoire de Matière Condensée et Sciences Interdisciplinaires, Faculty of Sciences, Mohammed V University of Rabat, Rabat 1014, Morocco
- Université de Lorraine, CNRS, GeoRessources, Nancy, 54000, France
| | - Mehdi Abbasi
- Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France.
| | | | - Chaouqi Misbah
- Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France.
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3
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Bureau L, Coupier G, Salez T. Lift at low Reynolds number. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:111. [PMID: 37957450 DOI: 10.1140/epje/s10189-023-00369-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2023] [Accepted: 10/19/2023] [Indexed: 11/15/2023]
Abstract
Lift forces are widespread in hydrodynamics. These are typically observed for big and fast objects and are often associated with a combination of fluid inertia (i.e. large Reynolds numbers) and specific symmetry-breaking mechanisms. In contrast, the properties of viscosity-dominated (i.e. low Reynolds numbers) flows make it more difficult for such lift forces to emerge. However, the inclusion of boundary effects qualitatively changes this picture. Indeed, in the context of soft and biological matter, recent studies have revealed the emergence of novel lift forces generated by boundary softness, flow gradients and/or surface charges. The aim of the present review is to gather and analyse this corpus of literature, in order to identify and unify the questioning within the associated communities, and pave the way towards future research.
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Affiliation(s)
- Lionel Bureau
- Univ. Grenoble Alpes, CNRS, LIPhy, 38000, Grenoble, France.
| | | | - Thomas Salez
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400, Talence, France.
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4
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Nouaman M, Darras A, John T, Simionato G, Rab MAE, van Wijk R, Laschke MW, Kaestner L, Wagner C, Recktenwald SM. Effect of Cell Age and Membrane Rigidity on Red Blood Cell Shape in Capillary Flow. Cells 2023; 12:1529. [PMID: 37296651 PMCID: PMC10252257 DOI: 10.3390/cells12111529] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Revised: 05/30/2023] [Accepted: 05/30/2023] [Indexed: 06/12/2023] Open
Abstract
Blood flow in the microcirculatory system is crucially affected by intrinsic red blood cell (RBC) properties, such as their deformability. In the smallest vessels of this network, RBCs adapt their shapes to the flow conditions. Although it is known that the age of RBCs modifies their physical properties, such as increased cytosol viscosity and altered viscoelastic membrane properties, the evolution of their shape-adapting abilities during senescence remains unclear. In this study, we investigated the effect of RBC properties on the microcapillary in vitro flow behavior and their characteristic shapes in microfluidic channels. For this, we fractioned RBCs from healthy donors according to their age. Moreover, the membranes of fresh RBCs were chemically rigidified using diamide to study the effect of isolated graded-membrane rigidity. Our results show that a fraction of stable, asymmetric, off-centered slipper-like cells at high velocities decreases with increasing age or diamide concentration. However, while old cells form an enhanced number of stable symmetric croissants at the channel centerline, this shape class is suppressed for purely rigidified cells with diamide. Our study provides further knowledge about the distinct effects of age-related changes of intrinsic cell properties on the single-cell flow behavior of RBCs in confined flows due to inter-cellular age-related cell heterogeneity.
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Affiliation(s)
- Mohammed Nouaman
- Dynamics of Fluids, Department of Experimental Physics, Saarland University, 66123 Saarbrücken, Germany
| | - Alexis Darras
- Dynamics of Fluids, Department of Experimental Physics, Saarland University, 66123 Saarbrücken, Germany
| | - Thomas John
- Dynamics of Fluids, Department of Experimental Physics, Saarland University, 66123 Saarbrücken, Germany
| | - Greta Simionato
- Dynamics of Fluids, Department of Experimental Physics, Saarland University, 66123 Saarbrücken, Germany
- Institute for Clinical and Experimental Surgery, Saarland University, 66421 Homburg, Germany
| | - Minke A. E. Rab
- Central Diagnostic Laboratory-Research, University Medical Center Utrecht, Utrecht University, 3584 CX Utrecht, The Netherlands
- Department of Hematology, University Medical Center Utrecht, Utrecht University, 3584 CX Utrecht, The Netherlands
| | - Richard van Wijk
- Central Diagnostic Laboratory-Research, University Medical Center Utrecht, Utrecht University, 3584 CX Utrecht, The Netherlands
| | - Matthias W. Laschke
- Institute for Clinical and Experimental Surgery, Saarland University, 66421 Homburg, Germany
| | - Lars Kaestner
- Dynamics of Fluids, Department of Experimental Physics, Saarland University, 66123 Saarbrücken, Germany
- Theoretical Medicine and Biosciences, Saarland University, 66421 Homburg, Germany
| | - Christian Wagner
- Dynamics of Fluids, Department of Experimental Physics, Saarland University, 66123 Saarbrücken, Germany
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Steffen M. Recktenwald
- Dynamics of Fluids, Department of Experimental Physics, Saarland University, 66123 Saarbrücken, Germany
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5
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Bedggood P, Ding Y, Metha A. Measuring red blood cell shape in the human retina. OPTICS LETTERS 2023; 48:1554-1557. [PMID: 37221708 DOI: 10.1364/ol.483062] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2022] [Accepted: 02/11/2023] [Indexed: 05/25/2023]
Abstract
The free diameter of a red blood cell generally exceeds the lumen diameter of capillaries in the central nervous system, requiring significant cellular deformation. However, the deformations undertaken are not well established under natural conditions due to the difficulty in observing corpuscular flow in vivo. Here we describe a novel, to the best of our knowledge, method to noninvasively study the shape of red blood cells as they traverse the narrow capillary networks of the living human retina, using high-speed adaptive optics. One hundred and twenty-three capillary vessels were analyzed in three healthy subjects. For each capillary, image data were motion-compensated and then averaged over time to reveal the appearance of the blood column. Data from hundreds of red blood cells were used to profile the average cell in each vessel. Diverse cellular geometries were observed across lumens ranging from 3.2 to 8.4 µm in diameter. As capillaries narrowed, cells transitioned from rounder to more elongated shapes and from being counter-aligned to aligned with the axis of flow. Remarkably, in many vessels the red blood cells maintained an oblique orientation relative to the axis of flow.
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6
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Wang C, Li J, Zhao L, Qian P. Shape transformations of red blood cells in the capillary and their possible connections to oxygen transportation. J Biol Phys 2022; 48:79-92. [PMID: 34799817 PMCID: PMC8866595 DOI: 10.1007/s10867-021-09594-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2021] [Accepted: 11/02/2021] [Indexed: 11/30/2022] Open
Abstract
In this work, a series of numerical simulations have been performed to obtain the steady shapes of red blood cells under a shear force field in the capillary. Two possible classes of steady shapes, the axisymmetric parachute and the non-axisymmetric parachute, are found. If we assume that oxygen diffusion across the red cell membrane is mediated by membrane curvature, it is found that the non-axisymmetric parachute will be more favorable due to its special shape which enables it to have a larger portion of membrane patch capable of releasing oxygen to tissues.
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Affiliation(s)
- Caiqun Wang
- Department of Physics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083 China ,Beijing Computing Center, Beijing, 100094 China
| | - Jianfeng Li
- Department of Macromolecular Science, the State Key Laboratory of Molecular Engineering of Polymers, Fudan University, Shanghai, China.
| | - Liutao Zhao
- College of Mechanical Engineering, Tianjin University, Tianjin, 300350 China ,Beijing Computing Center, Beijing, 100094 China
| | - Ping Qian
- Department of Physics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China.
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7
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Recktenwald SM, Graessel K, Maurer FM, John T, Gekle S, Wagner C. Red blood cell shape transitions and dynamics in time-dependent capillary flows. Biophys J 2022; 121:23-36. [PMID: 34896369 PMCID: PMC8758421 DOI: 10.1016/j.bpj.2021.12.009] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2021] [Revised: 11/13/2021] [Accepted: 12/06/2021] [Indexed: 01/07/2023] Open
Abstract
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.
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Affiliation(s)
- Steffen M. Recktenwald
- Dynamics of Fluids, Department of Experimental Physics, Saarland University, Saarbrücken, Germany,Corresponding author
| | - Katharina Graessel
- Biofluid Simulation and Modeling, Department of Physics, University of Bayreuth, Bayreuth, Germany
| | - Felix M. Maurer
- Dynamics of Fluids, Department of Experimental Physics, Saarland University, Saarbrücken, Germany
| | - Thomas John
- Dynamics of Fluids, Department of Experimental Physics, Saarland University, Saarbrücken, Germany
| | - Stephan Gekle
- Biofluid Simulation and Modeling, Department of Physics, University of Bayreuth, Bayreuth, Germany
| | - Christian Wagner
- Dynamics of Fluids, Department of Experimental Physics, Saarland University, Saarbrücken, Germany,Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg, Luxembourg
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8
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Gallen AF, Castro M, Hernandez-Machado A. Red blood cells in low Reynolds number flow: A vorticity-based characterization of shapes in two dimensions. SOFT MATTER 2021; 17:9587-9594. [PMID: 34651149 DOI: 10.1039/d1sm00559f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Studies on the mechanical properties of red blood cells improve the diagnosis of some blood-related diseases. Some existing numerical methods have successfully simulated the coupling between a fluid and red blood cells. This paper introduces an alternative phase-field model formulation of two-dimensional cells that solves the vorticity and stream function that simplifies the numerical implementation. We integrate red blood cell dynamics immersed in a Poiseuille flow and reproduce previously reported morphologies (slippers or parachutes). In the case of flow in a very wide channel, we discover a new metastable shape referred to as 'anti-parachute' that evolves into a horizontal slipper centered on the channel. This sort of metastable morphology may contribute to the dynamical response of the blood.
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Affiliation(s)
- Andreu F Gallen
- Departament Física de la Matèria Condensada, Universitat de Barcelona, E-08028 Barcelona, Spain.
| | - Mario Castro
- Instituto de Investigación Tecnológica (IIT), Universidad Pontificia Comillas, Madrid, E28015, Spain
| | - Aurora Hernandez-Machado
- Departament Física de la Matèria Condensada, Universitat de Barcelona, E-08028 Barcelona, Spain.
- Institute of Nanoscience and Nanotechnology (IN2UB), 08028 Barcelona, Spain
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9
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Takeishi N, Yamashita H, Omori T, Yokoyama N, Sugihara-Seki M. Axial and Nonaxial Migration of Red Blood Cells in a Microtube. MICROMACHINES 2021; 12:mi12101162. [PMID: 34683214 PMCID: PMC8541681 DOI: 10.3390/mi12101162] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/02/2021] [Revised: 09/22/2021] [Accepted: 09/24/2021] [Indexed: 11/18/2022]
Abstract
Human red blood cells (RBCs) are subjected to high viscous shear stress, especially during microcirculation, resulting in stable deformed shapes such as parachute or slipper shape. Those unique deformed RBC shapes, accompanied with axial or nonaxial migration, cannot be fully described according to traditional knowledge about lateral movement of deformable spherical particles. Although several experimental and numerical studies have investigated RBC behavior in microchannels with similar diameters as RBCs, the detailed mechanical characteristics of RBC lateral movement—in particular, regarding the relationship between stable deformed shapes, equilibrium radial RBC position, and membrane load—has not yet been fully described. Thus, we numerically investigated the behavior of single RBCs with radii of 4 μm in a circular microchannel with diameters of 15 μm. Flow was assumed to be almost inertialess. The problem was characterized by the capillary number, which is the ratio between fluid viscous force and membrane elastic force. The power (or energy dissipation) associated with membrane deformations was introduced to quantify the state of membrane loads. Simulations were performed with different capillary numbers, viscosity ratios of the internal to external fluids of RBCs, and initial RBC centroid positions. Our numerical results demonstrated that axial or nonaxial migration of RBC depended on the stable deformed RBC shapes, and the equilibrium radial position of the RBC centroid correlated well with energy expenditure associated with membrane deformations.
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Affiliation(s)
- Naoki Takeishi
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka 560-8531, Japan; (H.Y.); (M.S.-S.)
- Correspondence: ; Tel./Fax: +81-6-6850-6173
| | - Hiroshi Yamashita
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka 560-8531, Japan; (H.Y.); (M.S.-S.)
- Department of Pure and Applied Physics, Kansai University, 3-3-35 Yamate-cho, Suita 564-8680, Japan
| | - Toshihiro Omori
- Department of Finemechanics, Tohoku University, 6-6-01 Aoba, Sendai 980-8579, Japan;
| | - Naoto Yokoyama
- Department of Mechanical Engineering, Tokyo Denki University, 5 Senju-Asahi, Adachi, Tokyo 120-8551, Japan;
| | - Masako Sugihara-Seki
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka 560-8531, Japan; (H.Y.); (M.S.-S.)
- Department of Pure and Applied Physics, Kansai University, 3-3-35 Yamate-cho, Suita 564-8680, Japan
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10
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Yaya F, Römer J, Guckenberger A, John T, Gekle S, Podgorski T, Wagner C. Vortical flow structures induced by red blood cells in capillaries. Microcirculation 2021; 28:e12693. [PMID: 33666310 DOI: 10.1111/micc.12693] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Revised: 02/15/2021] [Accepted: 02/22/2021] [Indexed: 11/30/2022]
Abstract
OBJECTIVE 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. METHODS Red blood cells were injected in a 10 × 12 µm rectangular microchannel at a low hematocrit, and the flow field around one or two cells was captured by a high-speed camera that tracked 250 nm nanoparticles in the flow field, acting as tracers. RESULTS While the flow field around a steady "croissant" shape is found to be similar to that of a rigid sphere, the flow field around a "slipper" shape exhibits a small vortex at the rear of the red blood cell. Even more pronounced are vortex-like structures observed in the central region between two neighboring croissants. CONCLUSIONS The rotation frequency of the vortices is to a good approximation, inversely proportional to the distance between the cells. Our experimental data are complemented by numerical simulations.
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Affiliation(s)
- François Yaya
- Experimental Physics, Saarland University, Saarbrücken, Germany.,Laboratoire Interdisciplinaire de Physique, Saint Martin d'Hères, France
| | - Johannes Römer
- Biofluid Simulation and Modeling, Theoretische Physik VI, Universität Bayreuth, Bayreuth, Germany
| | - Achim Guckenberger
- Biofluid Simulation and Modeling, Theoretische Physik VI, Universität Bayreuth, Bayreuth, Germany
| | - Thomas John
- Experimental Physics, Saarland University, Saarbrücken, Germany
| | - Stephan Gekle
- Biofluid Simulation and Modeling, Theoretische Physik VI, Universität Bayreuth, Bayreuth, Germany
| | - Thomas Podgorski
- Laboratoire Interdisciplinaire de Physique, Saint Martin d'Hères, France
| | - Christian Wagner
- Experimental Physics, Saarland University, Saarbrücken, Germany.,Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg City, Luxembourg
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11
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Reichel F, Mauer J, Nawaz AA, Gompper G, Guck J, Fedosov DA. High-Throughput Microfluidic Characterization of Erythrocyte Shapes and Mechanical Variability. Biophys J 2019; 117:14-24. [PMID: 31235179 DOI: 10.1016/j.bpj.2019.05.022] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Revised: 05/03/2019] [Accepted: 05/22/2019] [Indexed: 02/01/2023] Open
Abstract
The motion of red blood cells (RBCs) in microchannels is important for microvascular blood flow and biomedical applications such as blood analysis in microfluidics. The current understanding of the complexity of RBC shapes and dynamics in microchannels is mainly based on several simulation studies, but there are a few systematic experimental investigations. Here, we present a combined study that systematically characterizes RBC behavior for a wide range of flow rates and channel sizes. Even though simulations and experiments generally show good agreement, experimental observations demonstrate that there is no single well-defined RBC state for fixed flow conditions but rather a broad distribution of states. This result can be attributed to the inherent variability in RBC mechanical properties, which is confirmed by a model that takes the variation in RBC shear elasticity into account. This represents a significant step toward a quantitative connection between RBC behavior in microfluidic devices and their mechanical properties, which is essential for a high-throughput characterization of diseased cells.
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Affiliation(s)
- Felix Reichel
- Biotechnology Center, Center for Molecular and Cellular Bioengineering, Technische Universität Dresden, Dresden, Germany
| | - Johannes Mauer
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich, Germany
| | - Ahmad Ahsan Nawaz
- Biotechnology Center, Center for Molecular and Cellular Bioengineering, Technische Universität Dresden, Dresden, Germany; School of Mechanical and Manufacturing Engineering, National University of Sciences and Technology, Islamabad, Pakistan
| | - Gerhard Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich, Germany
| | - Jochen Guck
- Biotechnology Center, Center for Molecular and Cellular Bioengineering, Technische Universität Dresden, Dresden, Germany; Max Planck Institute for the Science of Light, Erlangen, Germany.
| | - Dmitry A Fedosov
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, Jülich, Germany.
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12
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Takeishi N, Ito H, Kaneko M, Wada S. Deformation of a Red Blood Cell in a Narrow Rectangular Microchannel. MICROMACHINES 2019; 10:E199. [PMID: 30901883 PMCID: PMC6470855 DOI: 10.3390/mi10030199] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/14/2019] [Revised: 03/15/2019] [Accepted: 03/16/2019] [Indexed: 01/14/2023]
Abstract
The deformability of a red blood cell (RBC) is one of the most important biological parameters affecting blood flow, both in large arteries and in the microcirculation, and hence it can be used to quantify the cell state. Despite numerous studies on the mechanical properties of RBCs, including cell rigidity, much is still unknown about the relationship between deformability and the configuration of flowing cells, especially in a confined rectangular channel. Recent computer simulation techniques have successfully been used to investigate the detailed behavior of RBCs in a channel, but the dynamics of a translating RBC in a narrow rectangular microchannel have not yet been fully understood. In this study, we numerically investigated the behavior of RBCs flowing at different velocities in a narrow rectangular microchannel that mimicked a microfluidic device. The problem is characterized by the capillary number C a , which is the ratio between the fluid viscous force and the membrane elastic force. We found that confined RBCs in a narrow rectangular microchannel maintained a nearly unchanged biconcave shape at low C a , then assumed an asymmetrical slipper shape at moderate C a , and finally attained a symmetrical parachute shape at high C a . Once a RBC deformed into one of these shapes, it was maintained as the final stable configurations. Since the slipper shape was only found at moderate C a , measuring configurations of flowing cells will be helpful to quantify the cell state.
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Affiliation(s)
- Naoki Takeishi
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan.
| | - Hiroaki Ito
- Department of Mechanical Engineering, Osaka University, Suita, Osaka 565-0871, Japan.
- Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522, Japan.
| | - Makoto Kaneko
- Department of Mechanical Engineering, Osaka University, Suita, Osaka 565-0871, Japan.
| | - Shigeo Wada
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan.
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13
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Hogan B, Shen Z, Zhang H, Misbah C, Barakat AI. Shear stress in the microvasculature: influence of red blood cell morphology and endothelial wall undulation. Biomech Model Mechanobiol 2019; 18:1095-1109. [PMID: 30840162 DOI: 10.1007/s10237-019-01130-8] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2018] [Accepted: 02/09/2019] [Indexed: 01/26/2023]
Abstract
The effect of red blood cells and the undulation of the endothelium on the shear stress in the microvasculature is studied numerically using the lattice Boltzmann-immersed boundary method. The results demonstrate a significant effect of both the undulation of the endothelium and red blood cells on wall shear stress. Our results also reveal that morphological alterations of red blood cells, as occur in certain pathologies, can significantly affect the values of wall shear stress. The resulting fluctuations in wall shear stress greatly exceed the nominal values, emphasizing the importance of the particulate nature of blood as well as a more realistic description of vessel wall geometry in the study of hemodynamic forces. We find that within the channel widths investigated, which correspond to those found in the microvasculature, the inverse minimum distance normalized to the channel width between the red blood cell and the wall is predictive of the maximum wall shear stress observed in straight channels with a flowing red blood cell. We find that the maximum wall shear stress varies several factors more over a range of capillary numbers (dimensionless number relating strength of flow to membrane elasticity) and reduced areas (measure of deflation of the red blood cell) than the minimum wall shear stress. We see that waviness reduces variation in minimum and maximum shear stresses among different capillary and reduced areas.
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Affiliation(s)
- Brenna Hogan
- Hydrodynamics Laboratory (LadHyX), École Polytechnique, Palaiseau, France
| | - Zaiyi Shen
- Laboratoire Ondes et Matière d'Aquitaine (LOMA), Université de Bordeaux, Talence, France
| | - Hengdi Zhang
- Laboratoire Interdisciplinaire de Physique (LiPhy), Université Joseph Fourier, Saint-Martin-d'Hères, France
| | - Chaouqi Misbah
- Laboratoire Interdisciplinaire de Physique (LiPhy), Université Joseph Fourier, Saint-Martin-d'Hères, France
| | - Abdul I Barakat
- Hydrodynamics Laboratory (LadHyX), École Polytechnique, Palaiseau, France.
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14
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Guruprasad P, Mannino RG, Caruso C, Zhang H, Josephson CD, Roback JD, Lam WA. Integrated automated particle tracking microfluidic enables high-throughput cell deformability cytometry for red cell disorders. Am J Hematol 2019; 94:189-199. [PMID: 30417938 DOI: 10.1002/ajh.25345] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2018] [Revised: 11/02/2018] [Accepted: 11/06/2018] [Indexed: 12/17/2022]
Abstract
Investigating individual red blood cells (RBCs) is critical to understanding hematologic diseases, as pathology often originates at the single-cell level. Many RBC disorders manifest in altered biophysical properties, such as deformability of RBCs. Due to limitations in current biophysical assays, there exists a need for high-throughput analysis of RBC deformability with single-cell resolution. To that end, we present a method that pairs a simple in vitro artificial microvasculature network system with an innovative MATLAB-based automated particle tracking program, allowing for high-throughput, single-cell deformability index (sDI) measurements of entire RBC populations. We apply our technology to quantify the sDI of RBCs from healthy volunteers, Sickle cell disease (SCD) patients, a transfusion-dependent beta thalassemia major patient, and in stored packed RBCs (pRBCs) that undergo storage lesion over 4 weeks. Moreover, our system can also measure cell size for each RBC, thereby enabling 2D analysis of cell deformability vs cell size with single cell resolution akin to flow cytometry. Our results demonstrate the clear existence of distinct biophysical RBC subpopulations with high interpatient variability in SCD as indicated by large magnitude skewness and kurtosis values of distribution, the "shifting" of sDI vs RBC size curves over transfusion cycles in beta thalassemia, and the appearance of low sDI RBC subpopulations within 4 days of pRBC storage. Overall, our system offers an inexpensive, convenient, and high-throughput method to gauge single RBC deformability and size for any RBC population and has the potential to aid in disease monitoring and transfusion guidelines for various RBC disorders.
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Affiliation(s)
- Puneeth Guruprasad
- Wallace H. Coulter Department of Biomedical Engineering; Georgia Institute of Technology and Emory University; Atlanta Georgia
| | - Robert G. Mannino
- Wallace H. Coulter Department of Biomedical Engineering; Georgia Institute of Technology and Emory University; Atlanta Georgia
- Aflac Cancer and Blood Disorder Center of Children's Healthcare of Atlanta, Department of Pediatrics; Emory University School of Medicine; Atlanta Georgia
| | - Christina Caruso
- Aflac Cancer and Blood Disorder Center of Children's Healthcare of Atlanta, Department of Pediatrics; Emory University School of Medicine; Atlanta Georgia
| | | | - Cassandra D. Josephson
- Department of Pathology and Laboratory Medicine; Emory University School of Medicine, Center for Transfusion and Cellular Therapies; Atlanta Georgia
| | - John D. Roback
- Department of Pathology and Laboratory Medicine; Emory University School of Medicine, Center for Transfusion and Cellular Therapies; Atlanta Georgia
| | - Wilbur A. Lam
- Wallace H. Coulter Department of Biomedical Engineering; Georgia Institute of Technology and Emory University; Atlanta Georgia
- Aflac Cancer and Blood Disorder Center of Children's Healthcare of Atlanta, Department of Pediatrics; Emory University School of Medicine; Atlanta Georgia
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15
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Kihm A, Kaestner L, Wagner C, Quint S. Classification of red blood cell shapes in flow using outlier tolerant machine learning. PLoS Comput Biol 2018; 14:e1006278. [PMID: 29906283 PMCID: PMC6021115 DOI: 10.1371/journal.pcbi.1006278] [Citation(s) in RCA: 47] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2018] [Revised: 06/27/2018] [Accepted: 06/06/2018] [Indexed: 12/16/2022] Open
Abstract
The manual evaluation, classification and counting of biological objects demands for an enormous expenditure of time and subjective human input may be a source of error. Investigating the shape of red blood cells (RBCs) in microcapillary Poiseuille flow, we overcome this drawback by introducing a convolutional neural regression network for an automatic, outlier tolerant shape classification. From our experiments we expect two stable geometries: the so-called 'slipper' and 'croissant' shapes depending on the prevailing flow conditions and the cell-intrinsic parameters. Whereas croissants mostly occur at low shear rates, slippers evolve at higher flow velocities. With our method, we are able to find the transition point between both 'phases' of stable shapes which is of high interest to ensuing theoretical studies and numerical simulations. Using statistically based thresholds, from our data, we obtain so-called phase diagrams which are compared to manual evaluations. Prospectively, our concept allows us to perform objective analyses of measurements for a variety of flow conditions and to receive comparable results. Moreover, the proposed procedure enables unbiased studies on the influence of drugs on flow properties of single RBCs and the resulting macroscopic change of the flow behavior of whole blood.
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Affiliation(s)
- Alexander Kihm
- Department of Experimental Physics, Saarland University, Campus E2 6, Saarbrücken, Germany
| | - Lars Kaestner
- Department of Experimental Physics, Saarland University, Campus E2 6, Saarbrücken, Germany
- Theoretical Medicine and Biosciences, Saarland University, Campus University Hospital, Homburg, Germany
| | - Christian Wagner
- Department of Experimental Physics, Saarland University, Campus E2 6, Saarbrücken, Germany
- Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg City, Luxembourg
| | - Stephan Quint
- Department of Experimental Physics, Saarland University, Campus E2 6, Saarbrücken, Germany
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16
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Guckenberger A, Kihm A, John T, Wagner C, Gekle S. Numerical-experimental observation of shape bistability of red blood cells flowing in a microchannel. SOFT MATTER 2018; 14:2032-2043. [PMID: 29473072 DOI: 10.1039/c7sm02272g] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
Red blood cells flowing through capillaries assume a wide variety of different shapes owing to their high deformability. Predicting the realized shapes is a complex field as they are determined by the intricate interplay between the flow conditions and the membrane mechanics. In this work we construct the shape phase diagram of a single red blood cell with a physiological viscosity ratio flowing in a microchannel. We use both experimental in vitro measurements as well as 3D numerical simulations to complement the respective other one. Numerically, we have easy control over the initial starting configuration and natural access to the full 3D shape. With this information we obtain the phase diagram as a function of initial position, starting shape and cell velocity. Experimentally, we measure the occurrence frequency of the different shapes as a function of the cell velocity to construct the experimental diagram which is in good agreement with the numerical observations. Two different major shapes are found, namely croissants and slippers. Notably, both shapes show coexistence at low (<1 mm s-1) and high velocities (>3 mm s-1) while in-between only croissants are stable. This pronounced bistability indicates that RBC shapes are not only determined by system parameters such as flow velocity or channel size, but also strongly depend on the initial conditions.
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Affiliation(s)
- Achim Guckenberger
- Biofluid Simulation and Modeling, Theoretische Physik, Universität Bayreuth, Germany.
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17
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Ye T, Shi H, Phan-Thien N, Lim CT, Li Y. Relationship between transit time and mechanical properties of a cell through a stenosed microchannel. SOFT MATTER 2018; 14:533-545. [PMID: 29308825 DOI: 10.1039/c7sm01891f] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The changes in the mechanical properties of a cell are not only the cause of some diseases, but can also be a biomarker for some disease states. In recent times, microfluidic devices with built-in constrictions have been widely used to measure these changes. The transit time in such devices, defined as the time that a cell takes to pass through a constriction, has been found to be a crucial factor associated with the cell mechanical properties. Here, we use smoothed dissipative particle dynamics (SDPD), a particle-based numerical method, to explore the relationship between the transit time and mechanical properties of a cell. Three expressions of the transit time are developed from our simulation data, with respect to the stenosed size of constrictions, the shear modulus and bending modulus of cells, respectively. We show that a convergent constriction (the inlet is wider than the outlet), and a sharp-corner constriction (the constriction outlet is narrow) are better in identifying the differences in the transit time of cells. Moreover, the transit time increases and gradually approaches a constant as the shear modulus of cells increases, but increases first and then decreases as the bending modulus increases. These results suggest that the mechanical properties of cells can indeed be measured by analyzing their transit time, based on the recommended microfluidic device.
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Affiliation(s)
- Ting Ye
- Department of Computational Mathematics, Jilin University, China.
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18
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Ye T, Phan-Thien N, Lim CT, Li Y. Red blood cell motion and deformation in a curved microvessel. J Biomech 2017; 65:12-22. [PMID: 29102268 DOI: 10.1016/j.jbiomech.2017.09.027] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2017] [Revised: 08/23/2017] [Accepted: 09/25/2017] [Indexed: 11/24/2022]
Abstract
The flow of cells through curved vessels is often encountered in various biomedical and bioengineering applications, such as red blood cells (RBCs) passing through the curved arteries in circulation, and cells sorting through a shear-induced migration in a curved channels. Most of past numerical studies focused on the cell deformation in small straight microvessels, or on the flow pattern in large curved vessels without considering the cell deformation. However, there have been few attempts to study the cell deformation and the associated flow pattern in a curved microvessel. In this work, a particle-based method, smoothed dissipative particle dynamics (SDPD), is used to simulate the motion and deformation of a RBC in a curved microvessel of diameter comparable to the RBC diameter. The emphasis is on the effects of the curvature, the type and the size of the curved microvessel on the RBC deformation and the flow pattern. The simulation results show that a small curved shape of the microvessel has negligible effect on the RBC behavior and the flow pattern which are similar to those in a straight microvessel. When the microvessel is high in curvature, the secondary flow comes into being with a pair of Dean vortices, and the velocity profile of the primary flow is skewed toward the inner wall of the microvessel. The RBC also loses the axisymmetric deformation, and it is stretched first and then shrinks when passing through the curved part of the microvessel with the large curvature. It is also found that a pair of Dean vortices arise only under the condition of De>1 (De is the Dean number, a ratio of centrifugal to viscous competition). The Dean vortices are more easily observed in the larger or more curved microvessels. Finally, it is observed that the velocity profile of primary flow is skewed toward the inner wall of curved microvessel, i.e., the fluid close to the inner wall flows faster than that close to the outer wall. This is contrary to the common sense in large curved vessels. This velocity skewness was found to depend on the curvature of the microvessel, as well as the viscous and inertial forces.
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Affiliation(s)
- Ting Ye
- Department of Computational Mathematics, Jilin University, China.
| | - Nhan Phan-Thien
- Department of Mechanical Engineering, National University of Singapore, Singapore
| | - Chwee Teck Lim
- Department of Mechanical Engineering, National University of Singapore, Singapore; Department of Biomedical Engineering, National University of Singapore, Singapore; Mechanobiology Institute, National University of Singapore, Singapore
| | - Yu Li
- Department of Computational Mathematics, Jilin University, China
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19
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20
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21
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Lázaro GR, Hernández-Machado A, Pagonabarraga I. Rheology of red blood cells under flow in highly confined microchannels: I. effect of elasticity. SOFT MATTER 2014; 10:7195-206. [PMID: 25105872 DOI: 10.1039/c4sm00894d] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
We analyze the rheology of dilute red blood cell suspensions in pressure driven flows at low Reynolds number, in terms of the morphologies and elasticity of the cells. We focus on narrow channels of width similar to the cell diameter, when the interactions with the walls dominate the cell dynamics. The suspension presents a shear-thinning behaviour, with a Newtonian-behaviour at low shear rates, an intermediate region of strong decay of the suspension viscosity, and an asymptotic regime at high shear rates in which the effective viscosity converges to that of the solvent. We identify the relevant aspects of cell elasticity that contribute to the rheological response of blood at high confinement. In a second paper, we will explore the focusing of red blood cells while flowing at high shear rates and how this effect is controlled by the geometry of the channel.
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Affiliation(s)
- Guillermo R Lázaro
- Departament d'Estructura i Constituents de la Materia, Universitat de Barcelona, Av. Diagonal 647, E08028 Barcelona, Spain.
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22
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Aouane O, Thiébaud M, Benyoussef A, Wagner C, Misbah C. Vesicle dynamics in a confined Poiseuille flow: from steady state to chaos. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:033011. [PMID: 25314533 DOI: 10.1103/physreve.90.033011] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2014] [Indexed: 06/04/2023]
Abstract
Red blood cells (RBCs) are the major component of blood, and the flow of blood is dictated by that of RBCs. We employ vesicles, which consist of closed bilayer membranes enclosing a fluid, as a model system to study the behavior of RBCs under a confined Poiseuille flow. We extensively explore two main parameters: (i) the degree of confinement of vesicles within the channel and (ii) the flow strength. Rich and complex dynamics for vesicles are revealed, ranging from steady-state shapes (in the form of parachute and slipper shapes) to chaotic dynamics of shape. Chaos occurs through a cascade of multiple periodic oscillations of the vesicle shape. We summarize our results in a phase diagram in the parameter plane (degree of confinement and flow strength). This finding highlights the level of complexity of a flowing vesicle in the small Reynolds number where the flow is laminar in the absence of vesicles and can be rendered turbulent due to elasticity of vesicles.
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Affiliation(s)
- Othmane Aouane
- Department of Experimental Physics, Saarland University, 66123 Saarbrücken, Germany and Université Grenoble Alpes, LIPHY, F-38000 Grenoble, France and LMPHE, URAC 12, Faculté des Sciences, Université Mohammed V-Agdal, Rabat, Morocco
| | | | - Abdelilah Benyoussef
- LMPHE, URAC 12, Faculté des Sciences, Université Mohammed V-Agdal, Rabat, Morocco
| | - Christian Wagner
- Department of Experimental Physics, Saarland University, 66123 Saarbrücken, Germany
| | - Chaouqi Misbah
- Université Grenoble Alpes, LIPHY, F-38000 Grenoble, France
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23
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Fedosov DA, Peltomäki M, Gompper G. Deformation and dynamics of red blood cells in flow through cylindrical microchannels. SOFT MATTER 2014; 10:4258-67. [PMID: 24752231 DOI: 10.1039/c4sm00248b] [Citation(s) in RCA: 81] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
The motion of red blood cells (RBCs) in microcirculation plays an important role in blood flow resistance and in the cell partitioning within a microvascular network. Different shapes and dynamics of RBCs in microvessels have been previously observed experimentally including the parachute and slipper shapes. We employ mesoscale hydrodynamic simulations to predict the phase diagram of shapes and dynamics of RBCs in cylindrical microchannels, which serve as idealized microvessels, for a wide range of channel confinements and flow rates. A rich dynamical behavior is found, with snaking and tumbling discocytes, slippers performing a swinging motion, and stationary parachutes. We discuss the effects of different RBC states on the flow resistance, and the influence of RBC properties, characterized by the Föppl-von Kármán number, on the shape diagram. The simulations are performed using the same viscosity for both external and internal fluids surrounding a RBC; however, we discuss how the viscosity contrast would affect the shape diagram.
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Affiliation(s)
- Dmitry A Fedosov
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany.
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24
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Farutin A, Misbah C. Symmetry breaking and cross-streamline migration of three-dimensional vesicles in an axial Poiseuille flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042709. [PMID: 24827280 DOI: 10.1103/physreve.89.042709] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2013] [Indexed: 06/03/2023]
Abstract
We analyze numerically the problem of spontaneous symmetry breaking and migration of a three-dimensional vesicle [a model for red blood cells (RBCs)] in axisymmetric Poiseuille flow. We explore the three relevant dimensionless parameters: (i) capillary number, Ca, measuring the ratio between the flow strength over the membrane bending mode, (ii) the ratio of viscosities of internal and external liquids, λ, and (iii) the reduced volume, ν=[V/(4/3)π]/(A/4π)3/2 (A and V are the area and volume of the vesicle). The overall picture turns out to be quite complex. We find that the parachute shape undergoes spontaneous symmetry-breaking bifurcations into a croissant shape and then into slipper shape. Regarding migration, we find complex scenarios depending on parameters: The vesicles either migrate towards the center, or migrate indefinitely away from it, or stop at some intermediate position. We also find coexisting solutions, in which the migration is inwards or outwards depending on the initial position. The revealed complexity can be exploited in the problem of cell sorting out and can help understanding the evolution of RBCs' in vivo circulation.
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Affiliation(s)
- Alexander Farutin
- Université Grenoble I/CNRS, Laboratoire Interdisciplinaire de Physique/UMR5588, Grenoble F-38041, France
| | - Chaouqi Misbah
- Université Grenoble I/CNRS, Laboratoire Interdisciplinaire de Physique/UMR5588, Grenoble F-38041, France
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