Journal of Biorheology

, Volume 25, Issue 1–2, pp 36–42 | Cite as

Effects of inner solution viscosity and membrane stiffness on erythrocyte deformability on passing through a microchannel: prediction by two-dimensional simulation

  • Atsushi Kase
  • Kiyoshi Bando
  • Kenkichi Ohba
Original Article


We studied erythrocyte deformability in an effort to develop diagnostic methods based on its measurement and thus aid in the development of therapies for circulatory diseases. In the reported work, we performed two-dimensional numerical simulations of blood flow through a microchannel (MC) to evaluate erythrocyte deformability, applying the immersed boundary method to simulate erythrocyte movement and deformation. To evaluate deformability, MC transit capacity and shape recoverability were considered, defined as the time required to pass through the MC and the time constant during the shape-recovery process after exiting the MC, respectively. The simulation results showed that the erythrocyte MC transit time increased when the viscosity of the inner solution or the stiffness of the membrane increased. The time constant for erythrocyte shape recovery increased as the inner solution viscosity increased. In contrast, the time constant decreased as the erythrocyte membrane stiffness increased. These time-constant trends were in agreement with a theoretical equation derived using the Kelvin model and with previous experimental results. This diagnostic method of measuring erythrocyte shape recoverability and MC transit capacity is anticipated to have clinical application.


Erythrocyte deformability Shape recoverability Microchannel Transit capacity Kelvin model Immersed boundary method 



Part of this research was supported by a “Strategic Project to Support the Formation of Research Bases at Private Universities” Matching Fund Subsidy from MEXT 2008–2010.


  1. 1.
    Sugawara M, Maeda N. Hemorheology and blood flow. San Antonio: Corona; 2003.Google Scholar
  2. 2.
    Maeda N. The rheological properties and physiology of blood. J Physiol Soc Jpn. 2004;66(9):287–97.Google Scholar
  3. 3.
    Uyesaka N, Shio H. Erythrocyte deformability—a review on measurement methodology. J Jpn Soc Biorheol (B&R). 2004;18(1):12–22.Google Scholar
  4. 4.
    Shiga T, Maeda N, Kon K. Erythrocyte rheology. Crit Rev Oncol Hematol. 1990;10(1):9–48.CrossRefGoogle Scholar
  5. 5.
    Fischer TM. On the energy dissipation in a tank-treading human red blood cell. Biophys J. 1980;32:863–8.CrossRefGoogle Scholar
  6. 6.
    Evans EA, Skalak R. Mechanics and thermodynamics of biomembranes. USA: CRC; 1980.Google Scholar
  7. 7.
    Hochmuth RM, Worthy PR, Evans EA. Red cell extensional recovery and the determination of membrane viscosity. Biophys J. 1979;26:104–14.CrossRefGoogle Scholar
  8. 8.
    Tajikawa T, Ohba K, Higuchi K, Sakakibara C. Visualization and observation of deformation of human red blood cell passing through a micro-channel array as a model of human blood capillary. Trans Vis Soc Jpn. 2005;25(12):84–91.Google Scholar
  9. 9.
    Imamura Y, Tajikawa T, Ohba K. Measurement of the time constant of shape recovery of erythrocyte using a micro-channel technique—comparison of normal, hardened erythrocyte and erythrocyte ghost. In: Proceedings of the 22nd Bioengineering Conference, vol 15; 2010.Google Scholar
  10. 10.
    Tajikawa T, Ohba K, Imamura Y, Muranishi F. Evaluation of time constant of shape recovery of RBC using micro-channel technique—Influence of hardness of membrane and viscosity of internal fluid of RBC. In: Abstracts of the 49th Annual Conference of Japanese Society for Medical and Biological Engineering; 2010(CD-ROM).Google Scholar
  11. 11.
    Kase A, Kohri S, Tajikawa T, Bando K, Ohba K. The observations of the deformation behavior and internal flow of the erythrocytes passing through a micro channel by a two-dimensional numerical simulation. Trans Jpn Soc Mech Eng. 2010;76(772-B):2111–7.Google Scholar
  12. 12.
    Peskin CS. The immersed boundary method. Acta Numerica. 2002;11:479–517.CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Minamitani H, Kawamura T, Tsukada K, Iijima A, Sekizuka E, Oshio C. Measurement of elasticity of erythrocytes using atomic force microscope. Trans Inst Electrical Eng Jpn. 2002;122-C(9):1664–71.Google Scholar
  14. 14.
    Fung YC. Biomechanics mechanical properties of living tissues. Berlin: Springer; 1993.Google Scholar
  15. 15.
    Hirose Y, Iitsuka R, Shioiri T, Yamanishi Y, Arai F, Arai T, Higashimori M, Tadakuma K, Kaneko M. The high speed measurement of the cell stiffness. In: Proceedings of the 10th system integration division conference, pp 1655–8; 2009.Google Scholar

Copyright information

© Japanese Society of Biorheology 2011

Authors and Affiliations

  1. 1.Graduate School of Science and EngineeringKansai UniversitySuitaJapan
  2. 2.Faculty of Engineering ScienceKansai UniversitySuitaJapan

Personalised recommendations