MICROVASCULAR RESEARCH d,, 379-393 (1990) Two-Dimensional Analysis of Two-File Flow of Red Cells along Capillaries M. SUGIHARA-SEKI, T. W. SECOMB,* AND R. SKALAKt National Cardiovascular Center Research Institute, 5-7-l Fujishiro-dai, Suita, Osaka 565, Japan; *Department of Physiology, University of Arizona, Tucson, Arizona 85724; and tDepartment of AMES-Bioengineering, University of California, San Diego, La Jolla, California 92093 Received February 9, 1990 The effect of a tank-treading motion of the red cell membrane on a staggered “zipper”- type red cell flow in capillaries is examined, using a two-dimensional theoretical model. An approximately triangular cell with a thin flexible membrane enclosing a viscous fluid is adopted as a mode1 of the red cell. The motion of model red cells arranged periodically along a two-dimensional channel in an idealized zipper-type arrangement is analyzed nu- merically by a finite element method applied to the Stokes equations for the flow both inside and outside the model cells. It is shown that, if the viscosity ratio of the internal fluid to the suspending fluid is lower than a critical value, there exists a stable zipper-type arrangement of cells. In that arrangement, the cells remain stationary relative to each other with the membrane tank-treading. In contrast, inhibiting tank-treading by increasing the viscosity ratio above the critical value induces a cyclic oscillatory motion of red cells. The critical viscosity ratio increases if the channel is narrowed or if the spacing between cells is reduced. The present results suggest that the membrane tank-treading tends to stabilize zipper-type arrangements of red cells in capillaries at high hematocrit. o 1990 Academic PKSS, Inc. INTRODUCTION Observations of red cell suspensions flowing through capillary tubes have shown that red cells exhibit a single-file or a multi-file arrangement, depending on flow conditions (Gaehtgens et al., 1980). In two-file flow along capillaries, a typical interdigitating arrangement of mammalian red cells resembling a “zipper” has been observed. It is reported that the red cells in “zipper’‘-type flow have almost constant cell shapes and orientation during cell passage down the capillary tube, while the cell membrane continuously rotates around the cytoplasm (tank- treading) (Gaehtgens and Schmid-Schiinbein, 1982). Since rigidified mammalian cells and nucleated avian erythrocytes show substantial orientation instability when subjected to shear flow, such stability of zipper-type arrangements of mammalian red cells is speculated to be due to the membrane tank-treading. The purpose of the present study is to examine the contribution of membrane tank-treading motion to the flow resistance and flow stability of zipper-type arrangements of red cells in capillaries. A two-dimensional model is developed, in which an approximately triangular cell shape is prescribed, with a thin flexible membrane which is assumed to move uniformly along the perimeter. The motion of model red cells arranged periodically along a two-dimensional channel in this 379 0026.2862/90 $3.00 Copyright 0 1990 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in U.S.A.