OpenLB
Open Library of Bioscience
Advanced Search
International journal for numerical methods in biomedical engineering
11, 2019;35 (11): e3243.

Numerical simulation of deformable particles in a Coulter counter.

Pierre Taraconat, Jean-Philippe Gineys, Damien Isebe, Franck Nicoud, Simon Mendez
Author Information
  1. Pierre Taraconat: HORIBA Medical, Montpellier, France. ORCID
  2. Jean-Philippe Gineys: HORIBA Medical, Montpellier, France.
  3. Damien Isebe: HORIBA Medical, Montpellier, France.
  4. Franck Nicoud: Institut Montpelliérain Alexander Grothendieck, CNRS, University of Montpellier, Montpellier, France.
  5. Simon Mendez: Institut Montpelliérain Alexander Grothendieck, CNRS, University of Montpellier, Montpellier, France. ORCID
PMID: 31373760 DOI: 10.1002/cnm.3243

Abstract

In Coulter counters, cells counting and volumetry are achieved by monitoring their electrical print when they flow through a sensing zone. However, the volume measurement may be impaired by the cell dynamics, which may be difficult to control. In this paper, numerical simulations of the dynamics and electrical signature of red blood cells in a Coulter counter are presented, accounting for the deformability of the cells. In particular, a specific numerical pipeline is developed to overcome the challenge of the multi-scale nature of the problem. It consists in segmenting the whole computation of the cell dynamics and electrical response in a series of dedicated computations, with a saving of one order of magnitude in computational time. This numerical pipeline is used with rigid spheres and deformable red blood cells in an industrial Coulter counter geometry, and compared with experimental measurements. The simulations not only reproduce electrical signatures typical of those measured experimentally, but also allow an analysis of the electrical signature in terms of the heterogeneity of the electrical field and dynamics of the particles in the measurement zone. This study provides a methodology for computing the sizing of rigid or deformable particles by Coulter counters, opening the way to a better understanding of cells signatures in such devices.

Keywords

Coulter counter computational fluid dynamics fluid structure interaction immersed boundary method impedance measurement red blood cells

References

  1. Constantino BT. The red cell histogram and the dimorphic red cell population. Lab Med. 2011;42(5):300-308. https://doi.org/10.1309/LMF1UY85HEKBMIWO
  2. Gardner FH, Bessman JD, Gilmer J. Improved classification of anemias by MCV and RDW. Am J Clin Pathol. 1983;80(3):322-326. https://doi.org/10.1093/ajcp/80.3.322
  3. Yeşil A, Senateş E, Bayoğlu IV, Erdem ED, Demirtunç R, Kurdaş Övünç AO. Red cell distribution width: a novel marker of activity in inflammatory bowel disease. Gut Liver. 2011;5(22195244):460-467. https://www.ncbi.nlm.nih.gov/pmc/PMC3240789/
  4. Coulter WH. Means for Counting Particles suspended in a Fluid. U.S. Patent No. 2,656,508, Washington, DC,  U.S. Patent and Trademark Office.
  5. Grover NB, Naaman J, Ben-Sasson S, Doljanski F. Electrical sizing of particles in suspensions: I. theory. Biophys J. 1969;9:1398-1414.
  6. Hurley J. Sizing particles with a Coulter counter. Biophys J. 1970;10:74-79.
  7. Isèbe D, Nérin P. Numerical simulation of particle dynamics in an orifice-electrode system. Application to counting and sizing by impedance measurement. Int J Numer Methods Biomed Eng. 2013;29(4):462-475.
  8. Kachel V. Sizing of cells by the electrical resistance pulse technique: methodology and application in cytometric systems. Cell Anal. 1982;1:195-331.
  9. Velick S, Gorin M. The electrical conductance of suspensions of ellipsoids and its relation to the study of avian erythrocytes. J Gen Physiol. 1940;23(6):753-71.
  10. Breitmeyer MO, Lightfoot EN, Dennis WH. Model of red blood cell rotation in the flow toward a cell sizing orifice. Eur Biophys J. 1971;11:146-157.
  11. Qin Z, Zhe J, Wang G-X. Effects of particle's off-axis position, shape, orientation and entry position on resistance changes of micro coulter counting devices. Meas Sci Technol. 2011;22:45804.
  12. Golibersuch D. Observation of aspherical particle rotation in poiseuille flow via the resistance pulse technique: I. application to human erythrocytes. Biophys J. 1973;13(3):265-280. http://www.sciencedirect.com/science/article/pii/S0006349573859843
  13. Balogh P, Bagchi P. A computational approach to modeling cellular-scale blood flow in complex geometry. J Comput Phys. 2017;334:280-307. http://www.sciencedirect.com/science/article/pii/S0021999117300177
  14. Fedosov DA, Pan W, Caswell B, Gompper G, Karniadakis GE. Predicting human blood viscosity in silico. Proc Natl Acad Sci U S A. 2011;108(29):11772-11777.
  15. Freund JB. Numerical simulation of flowing blood cells. Annu Rev Fluid Mech. 2014;46:67-95.
  16. Matsunaga A, Imai Y, Wagner C, Ishikawa T. Reorientation of a single red blood cell during sedimentation. J Fluid Mech. 2016;806:102-128.
  17. Guo J, Pui TS, Rahman ARA, Kang Y. 3d numerical simulation of a coulter counter array with analysis of electrokinetic forces. Electrophoresis. 2013;34(3):417-424.
  18. Lanotte L, Mauer J, Mendez S, et al. Red cells' dynamic morphologies govern blood shear thinning under microcirculatory flow conditions. Proc Natl Acad Sci USA. 2016;113(47):13289-13294.
  19. Gibaud E. Numerical simulation of red blood cells flowing in a blood analyzer. Ph.D. Thesis: Université de Montpellier; 2015.
  20. Sigüenza J, Mendez S, Ambard D, et al. Validation of an immersed thick boundary method for simulating fluid-structure interactions of deformable membranes. J Comput Phys. 2016;322:723-746.
  21. Sigüenza J, Mendez S, Nicoud F. How should the optical tweezers experiment be used to characterize the red blood cell membrane mechanics? Biomech Model Mechanobiol. 2017;16:1645-1657.
  22. Mauer J, Mendez S, Lanotte L, et al. Flow-induced transitions of red blood cell shapes under shear. Phys Rev Lett. 2018;121:118103.
  23. Mendez S, Abkarian M. In-plane elasticity controls the full dynamics of red blood cells in shear flow. Phys Rev Fluids. 2018;3:101101(R).
  24. Mendez S, Gibaud E, Nicoud F. An unstructured solver for simulations of deformable particles in flows at arbitrary Reynolds numbers. J Comput Phys. 2014;256(1):465-483.
  25. Méndez Rojano R, Mendez S, Nicoud F. Introducing the pro-coagulant contact system in the numerical assessment of device-related thrombosis. Biomech Model Mechanobiol. 2018;17(3):815-826.
  26. Puiseux T, Sewonu A, Meyrignac O, et al. Reconciling PC-MRI and CFD: an in-vitro study. NMR Biomed. 2019;32(5):e4063.
  27. Zmijanovic V, Mendez S, Moureau V, Nicoud F. About the numerical robustness of biomedical benchmark cases: interlaboratory FDA's idealized medical device. Int J Numer Methods Biomed Eng. 2017;33(1):e02789:1-17.
  28. Moureau V, Domingo P, Vervisch L. Design of a massively parallel CFD code for complex geometries. CR Mec. 2011;339(2-3):141-148.
  29. Kim J, Moin P. Application of a fractional-step method to incompressible Navier-Stokes equations. J Comput Phys. 1985;59:308-323.
  30. Malandain M, Maheu N, Moureau V. Optimization of the deflated conjugate gradient algorithm for the solving of elliptic equations on massively parallel machines. J Comput Phys. 2013;238:32-47.
  31. Skalak R, Tozeren A, Zarda RP, Chien S. Strain energy function of red blood cell membranes. Biophys J. 1973;13:245-264.
  32. Helfrich W. Elastic properties of lipid bilayers: theory and possible experiments. Z Naturforsch. 1973;28 c:693-703.
  33. Charrier J-M, Shrivastava S, Wu R. Free and constrained inflation of elastic membranes in relation to thermoforming non-axisymmetric problems. J Strain Anal Eng Des. 1989;24(2):55-74.
  34. Zhong-can OY, Helfrich W. Bending energy of vesicle membranes: general expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders. Phys Rev A. 1989;39(10):5280-5288.
  35. Farutin A, Biben T, Misbah C. 3D numerical simulations of vesicle and inextensible capsule dynamics. J Comput Phys. 2014;275:539-568.
  36. Peskin CS. The immersed boundary method. Acta Numerica. 2002;11:479-517.
  37. Pinelli A, Naqavi IZ, Piomelli U, Favier J. Immersed-boundary methods for general finite-difference and finite-volume Navier-Stokes solvers. J Comput Phys. 2010;229:9073-9091.
  38. Unverdi SO, Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. J Comput Phys. 1992;100:25-37.
  39. Iss C, Midou D, Moreau A, et al. Self-organization of red blood cell suspensions under confined 2d flows. Soft Matter. 2019;15:2971-2980.
  40. Loiseau E, Massiera G, Mendez S, Aguilar Martinez P, Abkarian M. Microfluidic study of enhanced deposition of sickle cells at acute corners. Biophys J. 2015;108:2623-2632.
  41. Specogna R, Trevisan F. A discrete geometric approach to solving time independent Schrödinger equation. J Comput Phys. 2011;230:1370-1381.
  42. Abkarian M, Viallat A. Fluid-structure interactions in low-Reynolds-number flows. On the importance of red blood cells deformability in blood flow. London: Royal Society of Chemistry; 2016:347-462.
  43. Cordasco D, Yazdani, Bagchi P. Comparison of erythrocyte dynamics in shear flow under different stress-free configurations. Phys Fluids. 2014;26:41902.
  44. Kelemen C, Chien S, Artmann GM. Temperature transition of human hemoglobin at body temperature: Effects of calcium. Biophys J. 2001;80:2622-2630.
  45. Grover NB, Naaman J, Ben-Sasson S, Doljanski F. Electrical sizing of particles in suspensions: III. rigid spheroids and red blood cells. Biophys J. 1972;12:1099-1116.
  46. Kachel V. Electrical resistance pulse sizing: Coulter sizing. Flow cytometry and sorting, second edition. New York: Wiley-Liss, Inc.; 1990:45-80.
  47. Waterman CS, Atkinson EEJ, Wilkins BJ, Fischer CL, Kimzey SL. Improved measurement of erythrocyte volume distribution by aperture-counter signal analysis. Clin Chem. 1975;21(9):1201-1211.
  48. Kantsler V, Segre E, Steinberg V. Vesicle dynamics in time-dependent elongation flow: wrinkling instability. Phys Rev Lett. 2007;99:178102.
  49. Lac E, Barthès-Biesel D, Pelekasis NA, Tsamopoulos J. Spherical capsules in three-dimensional unbounded Stokes flows: effect of the membrane constitutive law and onset of buckling. J Fluid Mech. 2004;516:303-334.
  50. Hu X-Q, Salsac A-V, Barthès-Biesel D. Flow of a spherical capsule in a pore with circular or square cross-section. J Fluid Mech. 2012;705:176-194.
  51. Ramanujan S, Pozrikidis C. Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities. J Fluid Mech. 1998;361:117-143.
  52. Sui Y, Low HT, Chew YT, Roy P. Tank-treading, swinging, and tumbling of liquid-filled elastic capsules in shear flow. Phys Rev E. 2008;77:16310.
  53. Durst F, Ray S, Ünsal B, Bayoumi OA. The development lengths of laminar pipe and channel flows. J Fluids Eng. 2005;127(6):1154-1160. https://doi.org/10.1115/1.2063088
  54. Zheng Y, Shojaei-Baghini E, Azad A, Wang C, Sun Y. High-throughput biophysical measurement of human red blood cells. Lab Chip. 2012;12(14):2560-2567. http://doi.org/10.1039/C2LC21210B
  55. Qiang Y, Liu J, Du E. Dielectrophoresis testing of nonlinear viscoelastic behaviors of human red blood cells. Micromachines. 2018;9(1):21. http://www.mdpi.com/2072-666X/9/1/21
  56. Nodargi NA, Bisegna P, Caselli F. Effective computational modeling of erythrocyte electro-deformation. Meccanica. 2017;52(3):613-631. https://doi.org/10.1007/s11012-016-0424-0

MeSH Term

Electric Impedance
Electrochemical Techniques
Erythrocyte Deformability
Erythrocytes
Humans
Hydrodynamics
Models, Theoretical
Journal Article Research Support, Non-U.S. Gov't

Word Cloud

Created with Highcharts 10.0.0CoultercellselectricaldynamicscountermeasurementnumericalredblooddeformableparticlescounterszonemaycellsimulationssignaturepipelinecomputationalrigidsignaturesfluidcountingvolumetryachievedmonitoringprintflowsensingHowevervolumeimpaireddifficultcontrolpaperpresentedaccountingdeformabilityparticularspecificdevelopedovercomechallengemulti-scalenatureproblemconsistssegmentingwholecomputationresponseseriesdedicatedcomputationssavingoneordermagnitudetimeusedspheresindustrialgeometrycomparedexperimentalmeasurementsreproducetypicalmeasuredexperimentallyalsoallowanalysistermsheterogeneityfieldstudyprovidesmethodologycomputingsizingopeningwaybetterunderstandingdevicesNumericalsimulationstructureinteractionimmersedboundarymethodimpedance

Similar Articles

Cited By (4)