Mathematical modeling of electro-rotation spectra of small particles in liquid solutions: Application to human erythrocyte aggregates

Abstract

Electro-rotation can be used to determine the dielectric properties of cells, as well as to observe dynamic changes in both dielectric and morphological properties. Suspended biological cells and particles respond to alternating-field polarization by moving, deforming or rotating. While in linearly polarized alternating fields the particles are oriented along their axis of highest polarizability, in circularly polarized fields the axis of lowest polarizability aligns perpendicular to the plane of field rotation. Ellipsoidal models for cells are frequently applied, which include, beside sphere-shaped cells, also the limiting cases of rods and disks. Human erythrocyte cells, due to their particular shape, hardly resemble an ellipsoid. The additional effect of rouleaux formation with different numbers of aggregations suggests a model of circular cylinders of variable length. In the present study, the induced dipole moment of short cylinders was calculated and applied to rouleaux of human erythrocytes, which move freely in a suspending conductive medium under the effect of a rotating external field. Electro-rotation torque spectra are calculated for such aggregations of different length. Both the maximum rotation speeds and the peak frequencies of the torque are found to depend clearly on the size of the rouleaux. While the rotation speed grows with rouleaux length, the field frequency ν p is lowest for the largest cell aggregations where the torque shows a maximum.

Numerical modeling of motion trajectory and deformation behavior of a cell in a nonuniform electric field

“…26,27 A crucial factor, termed the Clausius-Mossotti ͑CM͒ factor, is defined as a measure of the DEP force acting on rigid particles. For example, the CM factor of a rigid spherical particle is given by 26,27 …”

“…In other words, the DEP force is independent of the polarity of the applied electric field, which is a well-known characteristic of DEP. 26,27 …”

A Stability Result on the Orientation of Red Blood Cells in the Venule Network

“…The problem is of practical importance since erythrocyte cell aggregation stems from the fact that rouleaux formation is caused by an increased blood concentration of fibrinogen, globulin or paraprotein. Associated clinical disorders include acute and chronic inflammatory disorders, macroglobulinemia, and multiple myeloma [25].…”

“…In a paper by Zehe et al [25] the authors investigated the response of suspended biological cells and particles to electro-rotation, i.e. the alternating field polarization by moving, deforming or rotating.…”

“…The assumption is made that a rouleaux formation of erythrocytes in the form of a cylinder, will be considered as a particle with length . The rouleaux formation of erythrocytes due to side by side adherence of several individual cells, translates into a cylindrical cell model of height = ν × b; where ν is the average number of cells in rouleaux and b is the thickness of a single cell [25]. We explicitly state here that in the case of biological cells, including erythrocyte cell aggregates, one must deviate from the ellipsoidal form to account for these specially shaped cells and a cylindrical shape has to be considered.…”