Mathematical model for biological cell deformation in a cylindrical pore

• Authors: Maciej Szwast , Teresa Suchecka , Wojciech Piątkiewicz
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

cell deformation; red blood cell; cell stamina

• Publisher: De Gruyter Open
• Journal: Chemical and Process Engineering
• Year: 2012
• Volume: 33
• Issue: 3
• Pages: 385-396

Dates

published

1 - 10 - 2012

received

accepted

online

31 - 10 - 2012

Contributors

author

Maciej Szwast

• Warsaw University of Technology, Department of Chemical and Process Engineering, Warynskiego 1, 00-645 Warsaw, Poland

author

Teresa Suchecka

• Warsaw University of Life Sciences, Department of Hydraulic Engineering and Environmental Reclamation, Nowoursynowska 166, 02-787, Warsaw Poland

author

Wojciech Piątkiewicz

• Warsaw University of Technology, Department of Chemical and Process Engineering, Warynskiego 1, 00-645 Warsaw, Poland

References

• 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]

Identifiers

DOI

10.2478/v10176-012-0034-x