Effects of shear rate and suspending medium viscosity on elongation of red cells tank‐treading in shear flow

Abstract

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.

Effects of shear rate and suspending viscosity on deformation and frequency of red blood cells tank-treading in shear flows

“…It is not convenient to apply information from such simulations for interpretation of experimental observations of the suspending viscosity effect, since both the capillary number G and the viscosity ratio l vary with the suspending viscosity h o . Also, as noticed by Fischer and Korzeniewski (2011), only few numerical studies considered viscosity ratios in the range in rheoscope experiments, and the results from these limit simulations are not helpful for understanding the experimental observations.…”

“…In addition, even within the same suspending medium, Fischer (2007) noticed that the f , _ g curves exhibit a slightly convex fashion, indicating the increase of f with _ g slows down at high shear rates. Furthermore, recently Fischer and Korzeniewski (2011) performed thoughtful examination on the cell deformation data of TT RBCs, and they found that the suspending viscosity h o plays a slightly more important role than the shear rate _ g in determining the cell deformation, especially for low viscosities h o , 70 cP. In spite of these careful experimental investigations, the underlying mechanisms are still not well understood (Fischer 2007;Fischer and Korzeniewski 2011).…”

“…Furthermore, recently Fischer and Korzeniewski (2011) performed thoughtful examination on the cell deformation data of TT RBCs, and they found that the suspending viscosity h o plays a slightly more important role than the shear rate _ g in determining the cell deformation, especially for low viscosities h o , 70 cP. In spite of these careful experimental investigations, the underlying mechanisms are still not well understood (Fischer 2007;Fischer and Korzeniewski 2011). Such experimental studies also suffer several inevitable technical difficulties, including measurement inaccuracy and intraindividual distributions of cell parameters in the sample.…”

“…As mentioned by Fischer (2007), the artificial deformation produced in these methods is different from that blood cells experience in the circulation situation, and the applicability of the cell properties obtained from such methods could be doubtful for modeling and simulating of blood flow behaviors. Another option is rheoscopy, where RBCs are suspended at low hematocrit in a high-viscosity solution, and the RBC elongation and rotation frequency are measured when the suspension is subjected to a simple shear flow in a rheoscope (a transparent cone-plate chamber) (Fischer et al 1978;Tran-Son-Tay et al 1984;Fischer 2007;Fischer and Korzeniewski 2011). With sufficient shear stress applied, the RBCs in a rheoscope undergo the socalled tank-treading (TT) motion, where the cell membrane rotates around the elongated cell in an approximately stable shape and the interior cytoplasm performs an eddy-like circulation flow (Fischer 2007;Zhang et al 2007;Sui et al 2008).…”

Threshold shear stress for the transition between tumbling and tank-treading of red blood cells in shear flow: dependence on the viscosity of the suspending medium

“…Fischer & Korzeniewski (2011) studied the elongation of TT red cells varyingγ and η 0 . They found a threshold in η 0 above which the elongation was independent of cellular viscosities.…”