Parametrization of the deformation curve as a tool for standardization and interpretation of ektacytometric measurements

In ektacytometry (or laser-diffractometry), the deformation of red blood cells subjected to a series of shear stresses in Couette flow (high to low) is measured. The shear stress dependency of the measured deformation index DI is called a “deformation curve” and depends upon membrane and cell properties.

We studied the relation between red cell rheology and the various stages of the deformation curve. We used this insight to introduce an empirical model to describe the deformation curve in parameters that represent characteristics of the curve.

The Deformation Curve is an S-shaped curve when the shear stress is plotted on a logarithmic scale, and found to be accurately described by:

DI(τ)=DI_min+(DI_max−DI_min)(τ/τ_i)^m/(τ/τ_i)^m+1].

The minimum deformation (DI_min) at low stress is determined by the orientation of undeformed cells. At intermediate stresses the DI is determined by both the orientation and the deformation. At these stresses the tank-treading is commonly believed to be important and is reflected in τ_i. This is confirmed by the sensitivity of τ_i to membrane deformability. At high stresses the orientation angle is small and DI_max is mainly determined by the constant surface area-to-volume ratio of the cells. Parameter m determines the slope at intermediate stresses but the relation with cell rheology is yet unclear.

Although the parameters cannot be independently linked to membrane or cell properties, the empirical model proved to be useful in describing deformation curves over a large range of red cell deformabilities. We think that such parametrization of the deformation curve will prove to be very useful in standardization of ektacytometric measurements for clinical purposes.