Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion

Using mechanical cell properties measured by micromanipulation, and a model of cell distortion in laminar flow fields, a method has been developed for predicting disruption of animal cells by laminar shear stresses. Predictions of the model were compared with measured losses of cell number and viability of TB/C3 murine hybridomas sheared in a cone and plate viscometer at shear rates up to 3950 s−1, and shear stresses up to 600 Nm−2, achieved by enhancement of viscosity with dextran. In all cases, the experimental, results and predictions were within 30%. Such excellent agreement suggests it might be possible to use micromanipulation measurements of animal cell mechanical properties to predict cell damage in more complex flow fields, such as those in bioreactors. © 1992 John Wiley & Sons, Inc.

Estimation of disruption of animal cells by laminar shear stress.

A model flow field representative of Kolmogorov eddies in turbulence is proposed, and its two parameters are expressed in terms of the known bioreactor variables epsilon, the rate of turbulent power dissipation, and nu, the fluid kinematic viscosity. The trajectory through this flow field of a small sphere representing a cell is determined, and from that the time-varying local shear rate can be found. This allows calculation of the shear stress at any point on the sphere's surface as it rotates in and moves through the model eddy. The maximum shear stress imposed on the cell by the surrounding turbulence has a range of 0.5-5 dyn/cm(2), and can be estimated by 5.33rho(epsilonnu)(1/2). The shear stress has two major frequency components with ranges of 1-4 and 20-80 s(-1); the higher frequency component is estimated by 0.678(epsilon/nu)(1/2). The rotation of the direction of the shear stress vector at each point on the cell's surface is also discussed. Two ways in which external stresses might affect cell growth are proposed.

Transient shear stresses on a suspension cell in turbulence.

This paper treats the steady flow fields generated inside and outside an initially circular, inextensible, cylindrical membrane filled with an incompressible viscous fluid when the membrane is placed in a two-dimensional shear flow of another viscous fluid. The Reynolds numbers of both the interior and exterior flows were assumed to be zero (‘creeping flow’), but no further approximations were made in the formulation. A series solution of the resulting free boundary-value problem in powers of a dimensionless shear rate parameter was constructed through fifth order. When combined with a conformal coordinate transformation this series gave accurate results for large deformations of the membrane (up to an aspect ratio of 2.5). The rather tedious algebraic manipulations required to obtain the series solution were done by computer with a symbol-manipulation program (reduce), which both formulated the boundary-value problems for each successive order and solved them. Results are presented which show how the shear rate and fluid viscosities influence the internal and external velocity and pressure fields, the membrane deformation and its ‘tank-treading’ frequency, and the membrane tension.This work demonstrates that classical perturbation techniques combined with computer algebra offer a useful alternative to purely numerical methods for problems of this type.

S.P. Sutera

Papers

Mathematical model of the velocity field external to a tank-treading red cell