Experimental Correlation for Erythrocyte Aggregation Rate in Population Balance Modeling
Red Blood Cells (RBCs) or erythrocytes tend to form chain-like aggregates under low shear rate called rouleaux. This is a reversible process and rouleaux disaggregate in high shear rates. Therefore, RBCs aggregation occurs in the microcirculation where low shear rates are present but does not occur under normal physiological conditions in large arteries. Numerical modeling of RBCs interactions is fundamental in analytical models of a blood flow in microcirculation. Population Balance Modeling (PBM) is particularly useful for studying problems where particles agglomerate and break in a two phase flow systems to find flow characteristics. In this method, the elementary particles lose their individual identity due to continuous destructions and recreations by break-up and agglomeration. The aim of this study is to find RBCs aggregation in a dynamic situation. Simplified PBM was used previously to find the aggregation rate on a static observation of the RBCs aggregation in a drop of blood under the microscope. To find aggregation rate in a dynamic situation we propose an experimental set up testing RBCs sedimentation. In this test, RBCs interact and aggregate to form rouleaux. In this configuration, disaggregation can be neglected due to low shear stress. A high-speed camera is used to acquire video-microscopic pictures of the process. The sizes of the aggregates and velocity of sedimentation are extracted using an image processing techniques. Based on the data collection from 5 healthy human blood samples, the aggregation rate was estimated as 2.7x103(±0.3 x103) 1/s.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1129964Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 518
 J. K. Wright Chesnutt, "Discrete-Element Model of Red Blood Cell Aggregation in Blood Flow," Ph. D. thesis University of Iowa, Iowa City, IA, 2009.
 O. Baskurt, B. Neu and H. J. Meiselman, Red Blood Cell Aggregation, Boca Raton, FL: CRC Press Taylor & Francis Group, 2012.
 A. Popel and P. Johnson, "Microcirculation and hemorheology," Annual Review of Fluid, pp. 37(1):43-69, 2005.
 H. L. Goldsmith, G. R. Cokelet and P. Gaehtgens, "Robin Fahraeus: evolution of his concepts in cardiovascular physiology," Am J Physiol, vol. 257, p. 1005–15, 1989.
 T. M. Geislinger and T. Franke, "Hydrodynamic lift of vesicles and red blood cells in flow — from Fåhræus & Lindqvist to microfluidic cell sorting," Advances in Colloid and Interface Science, vol. 208, p. 161–176, 2014.
 A. M. Robertson, A. Sequeira and R. Owens, "Rheological models for blood," in Hemodynamical Flows: Modeling, Analysis and Simulation, Verlag Italia, Milano, Springer, 2008, pp. 211-241.
 M. Bureau, J. C. Healy, J. C. Bourgoin and M. Joly, "Rheological hysteresis of blood at low shear rate," BioRheology, vol. 17, pp. 191-203, 1980.
 R. G. Owens, "A new microstructure-based constitutive model for human blood," J. Non-Newtonian Fluid Mech., vol. 140, pp. 57-70, 2006.
 T. Shiga, K. Imaizumi, N. Harada and M. Sekiya, " Kinetics of rouleaux formation using TV image analyzer. I. Human erythrocytes," American Journal of Physiology, vol. 245, pp. H252-H258, 1983.
 G. Barshtein, D. Wajnblum, and S. Yedgar, " Kinetics of Linear Rouleaux Formation Studied by Visual Monitoring of Red Cell Dynamic Organization," Biophysical Journal Volume 78 2470–2474, May 2000.
 S. Chen, G. Barshtein, B. Gavish, Y. Mahler and S. Yedgar, "Monitoring of red blood cell aggregability in a flow-chamber by computerized image analysis," in International and Eighth European Conference on Clinical Hemorheology, Vienna, Austria, 1993.
 S. Chen, B. Gavish, S. Zhang, Y. Mahler and S. Yedgar, "Monitoring of erythrocyte aggregate morphology under flow by computerized image analysis," Biorheology, vol. 32, no. 4, pp. 487-496, 1995.
 S. Jayavanth and M. Singh, "Computerized analysis of erythrocyte aggregation from sequential video-microscopic images under gravitational sedimentation," ITBM-RBM, vol. 25, no. 2, pp. 67-74, 2004.
 D. Ramkirishna, Population Balances: Theory and Applications to Particulate Systems in Engineering, Academic Press, 2000.
 M. V. Smoluchowski, "Veruch einer mathematischen theorie der koagulationkinetik kolloider losungen," Z. Phys. Chem., vol. 192, pp. 129-168, 1917.
 F. W. Wiegel, “A network model for viscoelastic fluids”, Physica, vol. 42, pp. 156–164, 1969.
 B. Forster, D. Van De Ville, J. Berent, D. Sage, M. Unser, "Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images," Microsc. Res. Tech., 65(1-2), pp. 33-42, September 2004.
 R. C. Gonzalez, R. E. Woods, “Digital Image Processing”, Second edition, Prentice Hall, Upper Saddle River, New Jersey.
 E. Ponder, "On sedimentation and rouleaux formation," Q. J. Exp. Physiol., vol. 16, p. 173–194, 1924.