Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl


Preferences help
enabled [disable] Abstract
Number of results
2012 | 33 | 3 | 385-396

Article title

Mathematical model for biological cell deformation in a cylindrical pore


Title variants

Languages of publication



Some studies show that cells are able to penetrate through pores that are smaller than cell size. It concerns especially Red Blood Cells but it also may concern different types of biological cells. Such penetration of small pores is a very significant problem in the filtration process, for example in micro- or ultrafiltration. Deformability of cells allows them to go through the porous membrane and contaminate permeate. This paper shows how cells can penetrate small cylindrical holes and tries to assess mechanical stress in a cell during this process. A new mathematical approach to this phenomenon was presented, based on assumptions that were made during the microscopic observation of Red Blood Cell aspiration into a small capillary. The computational model concerns Red Blood Cell geometry. The mathematical model allows to obtain geometrical relation as well as mechanical stress relations.









Physical description


1 - 10 - 2012
31 - 10 - 2012


  • Warsaw University of Technology, Department of Chemical and Process Engineering, Warynskiego 1, 00-645 Warsaw, Poland
  • Warsaw University of Life Sciences, Department of Hydraulic Engineering and Environmental Reclamation, Nowoursynowska 166, 02-787, Warsaw Poland
  • Warsaw University of Technology, Department of Chemical and Process Engineering, Warynskiego 1, 00-645 Warsaw, Poland


  • Abatti P.J., 1997. Determination of the red blood cells ability to traverse cylindrical pores. IEEE Trans. Biomed. Eng., 44, 209-212. DOI: 10.1109/10.554767.[Crossref]
  • Bronzino J.D. (Ed.), 2006. Biomedical engineering fundamentals. Taylor&Francis, Boca Raton.
  • Discher D.E., Boal D.H., Boey S.K., 1998. Simulations of the erythrocyte cytoskeleton at large deformation. II. Micropipete aspiration. Biophys. J., 75, 1584-1597. DOI: 10.1016/S0006-3495(98)74076-7.[Crossref]
  • Hochmuth R.M., 2000. Micropipette aspiration of living cells. J. Biomech., 33, 15-22.
  • Kuzman D., Svetina S., Waugh R.E., Zeks B., 2004. Elastic properties of the red blood cell membrane that determine echinocyte deformability. Eur. Biophys. J., 33, 1-15. DOI: 10.1007/s00249-003-0337-4.[Crossref]
  • Lebleu N., Roques C., Aimar P., Causserand C., 2009. Role of the cell-wall structure in the retention of bacteria by microfiltration membranes. J. Membr. Sci, 326, 178-185. DOI: 10.1016/j.memsci.2008.09.049.[WoS][Crossref]
  • Li J., Lykotrafitis G., Dao M., Suresh S., 2007. Cytoskeletal dynamics of human erythrocyte. Proc. Natl. Acad. Sci. USA, 104, 4937-4942. DOI: 10.1073/pnas.0700257104.[Crossref]
  • Secomb T.W., Hsu R., 1996. Analysis of red blood cell motion through cylindrical micropores: Effects of cell properties. Biohys. J., 71, 1095-1101. DOI: 10.1016/S0006-3495(96)79311-6.[Crossref]
  • Secomb T.W., Hsu R., Pries A.R., 1998. A model for blood cell motion in glycocalyx-lined capillaries. Am. J. Physiol. Heart Cir. Physiol., 274, H1016-H1022.
  • Secomb T.W., Hsu R., Pries A.R., 2001. Motion of red blood cells in a capillary with an endothelial surface layer: effect of flow velocity. Am. J. Physio.l Heart. Circ. Physiol., 281, H629-H636.
  • Shinde M.H., Kulkarni S.S., Musale D.A., Joshi S.G., 1999. Improvement of the water purification capability of poly(acrylonitrile) ultrafiltration membranes. J. Membr. Sci., 162, 9-22. DOI: 10.1016/S0376-7388(99)00100-3.[Crossref]
  • Suchecka T., Piątkiewicz W., Sosnowski T.R., 2005. Is the cell retention by MF membrane absolutely safe - a hypothetical model for cell deformation in a membrane pore. J. Membr. Sci., 250, 135-140. DOI: 10.1016/j.memsci.2004.08.035.[Crossref]
  • Wang Y., Hammes F., Duggelin M., Egli T., 2008. Influence of size, shape, and flexibility on bacterial passage through micropore membrane filters. Environ. Sci. Technol., 42, 6749-6754. DOI: 10.1021/es800720n.[WoS][Crossref]
  • Ye T., Li H., Lam K.Y., 2011. Motion, deformation and aggregation of two cells in a microchannel by dielectrophoresis. Electrophoresis, 32, 3147-3156. DOI: 10.1002/elps.201100240.[Crossref][WoS]

Document Type

Publication order reference


YADDA identifier

JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.