Elongation measurements of red cells subjected to simple shear flow are usually performed using a single suspending medium (viscosity g 0 ) and varying the mean shear rate ð _ cÞ. Such data are often plotted versus the shear stress ðs ¼ g 0 _ cÞ suggesting that the elongation scales with s. In this work, normal blood samples were tested in a rheoscope varying both g 0 and _ c. The ranges of _ c were chosen to restrict the elongation of the red cells to low values where the behavior is dominated by their intrinsic properties. It was found that the elongation scales with g s 0 _ c with s decreasing from two at g 0 5 20 mPas to unity at g 0 5 70 mPas. Above g 0 5 70 mPas, the elongation is therefore essentially determined by the membrane elasticity alone. A side observation was a large variation of the elongation both intraindividually and interindividually. '
International Society for Advancement of CytometryKey terms rheoscope; image processing; computer modeling; scaling behavior; shape distributions; share of cell viscosities A standard method to measure the mechanical properties of red cells is to suspend the cells in solutions much more viscous than blood plasma and to measure their elongation when the suspension is subjected to simple shear flow (1,2). In addition to being elongated, the membrane moves around the elongated shape thus inducing an eddy flow within the cytoplasm. The membrane motion has been termed tanktread motion (1). The elongation is usually quantified by an elongation index EI ¼ LÀB LþB , where L and B denote the length and the width of the elongated cell. Measurements of EI of different blood samples are usually performed using a constant viscosity of the suspending medium (g 0 ) under variation of the mean shear rate ð _ cÞ. Such data are often plotted versus the shear stress of the undisturbed shear flow ðs ¼ g 0 _ cÞ suggesting that EI scales with s. If, on the other hand, the same blood sample was tested varying both g 0 and _ c, it was shown that EI does not scale with s. Using four viscosities between 12 and 51 mPas, EI was found to scale with g 1:5 0 _ c (3). An exponent greater unity can also be inferred from other experimental results (4,5).To explain this finding, the following hypothesis is put forward. (i) Besides elastic stresses, viscous stresses resist an elongation of tank-treading red cells. (ii) A variable contribution of the viscous stresses being three dimensional in the cytoplasm and two dimensional in the membrane is responsible for an exponent greater unity.To rationalize the hypothesis, we consider the following experiment. We first measure EI with a certain set of _ c and g 0 . Then we decrease _ c by a certain amount and increase g 0 to such an extent that EI remains constant. The elastic stresses and bending moments in the membrane remain essentially constant as EI did not change.