Dielectrophoretic-field flow fractionation analysis of dielectric, density, and deformability characteristics of cells and particles

Abstract

Dielectrophoretic field-flow fractionation (DEP-FFF) has been used to discriminate between particles and cells based on their dielectric and density properties. However, hydrodynamic lift forces (HDLF) at flow rates needed for rapid separations were not accounted for in the previous theoretical treatment of the approach. Furthermore, no method was developed to isolate particle or cell physical characteristics directly from DEP-FFF elution data. An extended theory of DEP-FFF is presented that accounts for HDLF. With the use of DS19 erythroleukemia cells as model particles with frequency-dependent dielectric properties, it is shown that the revised theory accounts for DEP-FFF elution behavior over a wide range of conditions and is consistent with sedimentation-FFF when the DEP force is zero. Conducting four elution runs under specified conditions, the theory allows for the derivation of the cell density distribution and provides good estimates of the distributions of the dielectric properties of the cells and their deformability characteristics that affect HDLF. The approach allows for rapid profiling of the biophysical properties of cells, the identification and characterization of subpopulations, and the design of optimal DEP-FFF separation conditions. The extended DEP-FFF theory is widely applicable, and the parameter measurement methods may be adapted easily to other types of particles.

Fig. 1

Elution profiles of DS19 cells at a flow rate of 10 mL.min⁻¹ (wall sheer rate v̇₀ = 95 sec⁻¹) for FFF (no DEP field) and for DEP at different fixed frequencies. Above the crossover frequency (74 kHz) the elution profiles spread out and the peaks become ill-defined.

Fig. 2

(A) Relationship between the DEP-FFF elution time and frequency for DS19 cells (●) for different flow rates. At the crossover frequency f₀ the DEP force is zero and elution times correspond to those measured by conventional sedimentation-FFF (★). Solid lines show simulated elution characteristics based upon the analysis given in the text. Dotted lines show elution characteristics predicted by earlier theory that ignored hydrodynamic lift. (B) The Clausius-Mossotti factor reveals the relative DEP force experienced by cells as a function of DEP frequency. The influence of this on cell elution characteristics is evident in (A).

Fig. 3

Relationship between cell elution time and cell density for DEP-FFF at 15 kHz. Symbols represent measured elution times for beads of 1062 and 1070 kg.m⁻³, and for monocytes (M), lymphocytes (L), and erythrocytes (E). The solid line shows the calculated responses expected from the theory under the experimental conditions (Table 1). The cell density distribution can be derived by mapping the elution profile using the calculated response. The elution profile for DS19 cells at 15 kHz shown along the time axis is mapped to the corresponding cell density distribution along the density axis.

Fig. 4

Relationship between cell elution and the cell hydrodynamic geometry function calculated from the theory is shown by the solid curve using the density peak data from Fig. 3. Using this relationship, the cell elution distribution for DS19 under sedimentation-FFF conditions can be mapped to the corresponding hydrodynamic geometry function distribution.

Fig. 5

Simulations of the progression of a cell through a DEP-FFF channel under different experimental conditions. (A) With no DEP field, cells move by conventional sedimentation-FFF at a height determined by the balance of sedimentation and HDLF effects. Changes in the hydrodynamic geometry function F(S, M) impact the height and corresponding velocity with which cells travel. (B – D) Simulations of cell progress during a logarithmically-programmed sweep of the DEP field frequency from 160 kHz to 15 kHz over 600 seconds. At short times the DEP frequency greatly exceeds the cell crossover frequency f₀ and cells move at minimum velocity V_min. Later, cells move faster as the swept frequency passes through f₀. At still longer times the DEP frequency has fallen far below f₀, and cells moves at maximum velocity, V_max. (B) Increasing the cell density ρ_p decreases the maximum velocity V_max but leaves V_min unchanged. (C) Increasing the hydrodynamic geometry function F(S, M) increases V_min but leaves V_max unchanged. (D) Increasing the crossover frequency f₀ leaves V_max and V_min unchanged, but increases the time at which the transition of the velocities occurs.

Fig. 6

Cell biophysical properties may be derived from four independent measurements. A shows the displacement of cells through the DEP-FFF channel as a function of time under the influence of a low frequency DEP field. The frequency is set low enough that the cells attain maximum levitation and so their resulting velocities reflect their density. B the conventional sedimentation-FFF elution profile is measured with the DEP field off. C the DEP frequency is maintained far above the anticipated crossover frequency of the cells for a period T_int and then switched to the low frequency used for Run A. Cells travel at minimum velocity under the influence of hydrodynamic lift forces until the frequencies switch. D shows cell behavior during a 600 second sweep from 160 kHz to 15 kHz.

Fig. 7

Relationship between cell elution time and cell crossover frequency f₀ calculated for a cell density of 1054 kg.m⁻³ and a hydrodynamic geometry function of 0.11 (solid line). The elution profile for DEP frequency swept from 160 to 15 kHz, is shown on the elution time axis. The corresponding cell crossover frequency distribution is shown on the abscissa.