Mesh-Based Modeling of Individual Cells and Their Dynamics in Biological Fluids

  • Ivan Cimrák
  • Iveta Jančigová
  • Renáta Tóthová
  • Markus Gusenbauer
Chapter

Abstract

This text is aimed at providing both basic and advanced knowledge on the individual cell modeling in a flow. Besides the overview of various existing approaches, it is focused on mesh-based model and on its capabilities to cover complex mechano-elastic properties combined with adhesion and magnetic phenomena. We also describe validation procedures, offer an example of use of the model for better understanding of cell behavior and a short overview of future research directions.

References

  1. 1.
    Ahlrichs, P., Dunweg, B.: Lattice-Boltzmann simulation of polymer-solvent systems. Int. J. Mod. Phys. C 8, 1429–1438 (1998)CrossRefGoogle Scholar
  2. 2.
    Akoun, G., Yonnet, J.: 3D analytical calculation of the forces exerted between two cuboidal magnets. IEEE Trans. Magn. 20(5), 1962–1964 (1984). doi:10.1109/TMAG.1984.1063554 CrossRefGoogle Scholar
  3. 3.
    Alon, R., Chen, S., Puri, K., Finger, E., Springer, T.: The kinetics of L-selectin tethers and the mechanics of selectin-mediated rolling. J. Cell Biol. 138(5), 1169–1180 (1997)CrossRefGoogle Scholar
  4. 4.
    Arnold, A., Lenz, O., Kesselheim, S., Weeber, R., Fahrenberger, F., Roehm, D., Košovan, P., Holm, C.: ESPResSo 3.1—molecular dynamics software for coarse-grained models. In: Griebel, M., Schweitzer, M. (eds.) Meshfree Methods for Partial Differential Equations VI. Lecture Notes in Computational Science and Engineering, vol. 89, pp. 1–23. Springer, New York (2013)Google Scholar
  5. 5.
    Basu, H., Dharmadhikari, A.K., Dharmadhikari, J.A., Sharma, S., Mathur, D.: Tank treading of optically trapped red blood cells in shear flow. Biophys. J. 101, 1604–1612 (2011)CrossRefGoogle Scholar
  6. 6.
    Chen, S., Doolen, G.: Lattice-Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364 (1998). doi:10.1146/annurev.fluid.30.1.329 MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cimrák, I.: Cell-in-fluid research group (2015). http://cell-in-fluid.fri.uniza.sk
  8. 8.
    Cimrák, I.: A simplified model for dynamics of cell rolling and cell-surface adhesion. In: AIP Conference Proceedings, 1648, 210005 (2015). doi:10.1063/1.4912490
  9. 9.
    Cimrák, I., Gusenbauer, M., Jančigová, I.: An ESPResSo implementation of elastic objects immersed in a fluid. Comput. Phys. Commun. 185(3), 900–907 (2014). doi:10.1016/j.cpc.2013.12.013 CrossRefGoogle Scholar
  10. 10.
    Cimrák, I., Gusenbauer, M., Schrefl, T.: Modelling and simulation of processes in microfluidic devices for biomedical applications. Comput. Math. Appl. 64(3), 278–288 (2012)MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Cimrák, I., Jančigová, I., Bachratá, K., Bachratý, H.: On elasticity of spring network models used in blood flow simulations in ESPResSo. In: Bisschoff, M., Oñate, E., Owen, D., Ramm, E., Wriggers, P. (eds.) III International Conference on Particle-based Methods—Fundamentals and Applications Particles 2013, pp. 133–144 (2013)Google Scholar
  12. 12.
    Cimrák, I., Tóthová, R., Jančigová, I.: Recent advances in mesh-based modeling of individual cells in biological fluids. In: 2014 10th International Conference on Digital Technologies (DT), pp. 25–31 (2014)Google Scholar
  13. 13.
    Dao, M., Li, J., Suresh, S.: Molecularly based analysis of deformation of spectrin network and human erythrocyte. Mater. Sci. Eng. C 26, 1232–1244 (2006)CrossRefGoogle Scholar
  14. 14.
    Derby, N., Olbert, S.: Cylindrical magnets and ideal solenoids. Am. J. Phys. 78(3), 229–235 (2010). doi:10.1119/1.3256157
  15. 15.
    Dong, C., Lei, X.X.: Biomechanics of cell rolling: shear flow, cell-surface adhesion, and cell deformability. J. Biomech. 33(1), 35–43 (2000)CrossRefGoogle Scholar
  16. 16.
    Du, F., Baune, M., Thoming, J.: Insulator-based dielectrophoresis in viscous media—simulation of particle and droplet velocity. J. Biomech. 65, 452–458 (2007)Google Scholar
  17. 17.
    Dunweg, B., Ladd, A.J.C.: Lattice-Boltzmann simulations of soft matter systems. Adv. Polym. Sci. 221, 89–166 (2009)Google Scholar
  18. 18.
    Dupin, M., Halliday, I., Care, C., Alboul, L.: Modeling the flow of dense suspensions of deformable particles in three dimensions. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 75, 066707 (2007)Google Scholar
  19. 19.
    Evans, E., Waugh, R., Melnik, L.: Elastic area compressibility modulus of red cell membrane. Biophys. J. 16(6), 585–595 (1976)CrossRefGoogle Scholar
  20. 20.
    Fedosov, D.: Multiscale modeling of blood flow and soft matter. Ph.D. thesis, Brown University (2010)Google Scholar
  21. 21.
    Feng, Z.G., Michaelides, E.E.: Proteus: a direct forcing method in the simulations of particulate flows. J. Comput. Phys. 202, 20–51 (2005)Google Scholar
  22. 22.
    Fischer, T.M.: Shape memory of human red blood cells. Biophys J. 86(5), 3304–3313 (2004). doi:10.1016/S0006-3495(04)74378-7 CrossRefGoogle Scholar
  23. 23.
    Fåhraeus, R.: The suspension stability of the blood. Physiol. Rev. 9, 241–274 (1929)Google Scholar
  24. 24.
    Fåhraeus, R., Lindqvist, T.: The viscosity of blood in narrow capillary tubes. Am. J. Physiol. 96, 562–568 (1931)Google Scholar
  25. 25.
    Goldsmith, H.L.: Red cell motions and wall interactions in tube flow. Fed. Proc. 30, 1578–1590 (1971)Google Scholar
  26. 26.
    Gronowicz, G., Swift, H., Steck, T.L.: Maturation of the reticulocyte in vitro. J. Cell Sci. 71, 177–197 (1984)Google Scholar
  27. 27.
    Gusenbauer, M., Kovacs, A., Reichel, F., Exl, L., Bance, S., Ozelt, H., Schrefl, T.: Self-organizing magnetic beads for biomedical applications. J. Magn. Magn. Mater. 324(6), 977–982 (2012). doi:10.1016/j.jmmm.2011.09.034 CrossRefGoogle Scholar
  28. 28.
    Hayes, M.A., Polson, N.A., Garcia, A.A.: Active control of dynamic supraparticle structures in microchannels. Langmuir 17(9), 2866–2871 (2001). doi:10.1021/la001655g CrossRefGoogle Scholar
  29. 29.
    Holm, C., Arnold, A., Lenz, O., Kesselheim, S.: ESPResSo Documentation (2014). http://espressomd.org/wordpress/documentation
  30. 30.
    Hosseini, S.M., Feng, J.: A particle-based model for the transport of erythrocytes in capillaries. Chem. Eng. Sci. 64, 4488–4497 (2009)CrossRefGoogle Scholar
  31. 31.
    Inglis, D.W., Riehn, R., Austin, R.H., Sturm, J.C.: Continuous microfluidic immunomagnetic cell separation. Appl. Phys. Lett. 85, 5093–5095 (2004)CrossRefGoogle Scholar
  32. 32.
    Jančigová, I., Cimrák, I.: Non-uniform force allocation for area preservation in spring network models. Int. J. Numer. Meth. Biomed. Engng. In printGoogle Scholar
  33. 33.
    Jančigová, I., Tóthová, R.: Scalability of forces in mesh-based models of elastic objects. In: ELEKTRO 2014: 10th International Conference, pp. 562–566. IEEE (2014)Google Scholar
  34. 34.
    Krishnamurthy, S., Yadav, A., Phelan, P.E., Calhoun, R., Vuppu, A.K., Garcia, A.A., Hayes, M.A.: Dynamics of rotating paramagnetic particle chains simulated by particle dynamics, Stokesian dynamics and lattice-Boltzmann methods. Microfluid. Nanofluid. 5(1), 33–41 (2007). doi:10.1007/s10404-007-0214-z CrossRefGoogle Scholar
  35. 35.
    Lee, S., Ahn, K., Lee, S., Sun, K., Goedhart, P., Hardeman, M.: Shear induced damage of red blood cells monitored by the decrease of their deformability. Korea-Aust. Rheol. J. 16(3), 141–146 (2004)Google Scholar
  36. 36.
    MacMeccan, R.M.: Mechanistic effects of erythrocytes on platelet deposition in coronary thrombosis. Ph.D. thesis, Georgia Institute of Technology (2007)Google Scholar
  37. 37.
    Melle, S., Calderón, O.G., Rubio, M.A., Fuller, G.G.: Microstructure evolution in magnetorheological suspensions governed by mason number. Phys. Rev. E 68(4), 041503 (2003)Google Scholar
  38. 38.
    Melville, D., Paul, F., Roath, S.: Direct magnetic separation of red cells from whole blood. Nature 255, 706 (1975)Google Scholar
  39. 39.
    Mills, J.P., Qie, L., Dao, M., Lim, C.T., Suresh, S.: Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers. Mol. Cell. Biomech. 1(3), 169–180 (2004)Google Scholar
  40. 40.
    Molday, R.S., Yen, S.P.S., Rembaum, A.: Applications of magnetic microspheres in labeling and separation of cells. Nature 268, 437–438 (1977)CrossRefGoogle Scholar
  41. 41.
    Nakamura, M., Bessho, S., Wada, S.: Spring network based model of a red blood cell for simulating mesoscopic blood flow. Int. J. Numer. Method Biomed. Eng. 29(1), 114–128 (2013). doi:10.1002/cnm.2501 MathSciNetCrossRefGoogle Scholar
  42. 42.
    Paul, F., Melville, D., Roath, S., Warhurst, D.C.: A bench top separator for malarial parasite concentration. IEEE Trans. Magn. MAG-17, 2822–2824 (1981)Google Scholar
  43. 43.
    Peskin, C.S.: The immersed boundary method. Acta Numerica 11, 479–517 (2002)Google Scholar
  44. 44.
    Philippova, O., Barabanova, A., Molchanov, V., Khokhlov, A.: Magnetic polymer beads: recent trends and developments in synthetic design and applications. Eur. Polym. J. 47(4), 542–559 (2011). doi:10.1016/j.eurpolymj.2010.11.006 CrossRefGoogle Scholar
  45. 45.
    Popel, A.S., Johnson, P.C.: Microcirculation and hemorheology. Annu. Rev. Fluid Mech. 37, 43–69 (2005)MathSciNetCrossRefGoogle Scholar
  46. 46.
    Pratt, E., Huang, C., Hawkins, B., Gleghorn, J., Kirby, B.J.: Rare cell capture in microfluidic devices. Chem. Eng. Sci. 66(7), 1508–1522 (2011)Google Scholar
  47. 47.
    Rahimian, A., Lashuk, I., Veerapaneni, S., Chandramowlishwaran, A., Malhotra, D., Moon, L., Sampath, R., Shringarpure, A., Vetter, J., Vuduc, R., Zorin, D., Biros, G.: Petascale direct numerical simulation of blood flow on 200k cores and heterogeneous architectures. In: Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis, SC ’10, pp. 1–11. IEEE Computer Society, Washington, DC, USA (2010). doi:10.1109/SC.2010.42
  48. 48.
    Rejniak, K.A.: Investigating dynamical deformations of tumor cells in circulation: predictions from a theoretical model. Front. Oncol. 2, 111 (2012)Google Scholar
  49. 49.
    Skalak, R., Branemark, P.: Deformation of red blood cells in capillaries. Science 164, 717–719 (1969)CrossRefGoogle Scholar
  50. 50.
    Taylor, C.A., Hughes, T.J., Zarins, C.K.: Finite element modeling of blood flow in arteries. Comput. Methods Appl. Mech. Eng. 158(1–2), 155–196 (1998). doi:10.1016/S0045-7825(98)80008-X MATHMathSciNetCrossRefGoogle Scholar
  51. 51.
    Tóthová, R., Cimrák, I.: Local stress analysis of red blood cells in shear flow. In: AIP Conference Proceedings, 1648, 210003 (2015). doi:10.1063/1.4912488
  52. 52.
    Tóthová, R., Jančigová, I., Cimrák, I.: Energy contributions of different elastic moduli in mesh-based modeling of deformable object. In: ELEKTRO 2014: 10th International Conference, pp. 634–638. IEEE (2014)Google Scholar
  53. 53.
    Tsubota, K., Wada, S.: Elastic force of red blood cell membrane during tank-treading motion: consideration of the membrane’s natural state. Int. J. Mech. Sci. 52, 356–364 (2010)CrossRefGoogle Scholar
  54. 54.
    Wang, L., Lu, J., Marchenko, S., Monuki, E., Flanagan, L., Lee, A.: Dual frequency dielectrophoresis with interdigitated sidewall electrodes for microfluidic flow-through separation of beads and cells. Electrophoresis 30, 782–791 (2009)CrossRefGoogle Scholar
  55. 55.
    Xu, D., Kaliviotis, E., Munjiza, A., Avital, E., Ji, C., Williams, J.: Large scale simulation of red blood cell aggregation in shear flows. J. Biomech. 46(11), 1810–1817 (2013). doi:10.1016/j.jbiomech.2013.05.010 CrossRefGoogle Scholar
  56. 56.
    Xu, Y., Philips, J., Yan, J., Li, Q., Fan, Z., Tan, W.: Aptamer-based microfluidic device for enrichment, sorting, and detection of multiple cancer cells. Analytical Chemistry 81, 7436–7442 (2009)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Ivan Cimrák
    • 1
  • Iveta Jančigová
    • 1
  • Renáta Tóthová
    • 1
  • Markus Gusenbauer
    • 2
  1. 1.Faculty of Management Science and InformaticsUniversity of ŽilinaŽilinaSlovakia
  2. 2.Center for Integrated Sensor SystemsDanube University KremsKrems an der DonauAustria

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