Dielectrophoretic Separation of Platelets from Red Blood Cells

By exploiting the fact that platelets are the smallest cells in blood, it is possible to perform size-based fractionation of blood (that is, separate platelets from red blood cells) using dielectrophoresis, a force produced by a spatially nonuniform electric field that can even affect electrically neutral particles. This model demonstrates the continuous separation of platelets from red blood cells (RBCs) using the feature available in the Particle Tracing for Fluid Flow interface.

Model Definition

Dielectrophoresis is the movement of particles in a nonuniform electric field due to the interaction of the particles’ induced dipoles with the spatial gradient of the electric field norm.

When the electric field is computed in the frequency domain, the feature adds the following contribution to the total force exerted on the particles:

where

•

rp (SI unit: m) is the radius of a spherical particle in the field,

•

ε0 = 8.854187817·10−12 F/m is the vacuum permittivity,

•

(dimensionless) is the complex relative permittivity of the fluid,

•

(dimensionless) is the complex relative permittivity of the particle, and

•

Erms (SI unit: V/m) is the root mean square electric field.

For fields that are computed in the frequency domain, the complex permittivity can be expressed as

where ε (SI unit: F/m) is the permittivity, σ (SI unit: S/m) is the electrical conductivity, and ω (SI unit: Hz) is the angular frequency of the electric field.

The subnode can be added to the node to model the dielectrophoretic (DEP) force on particles with thin dielectric shells. The complex permittivity of the shell can differ from the complex permittivity of the rest of the particle. When computing the dielectrophoretic force, the complex permittivity of the particle is replaced by the equivalent complex relative permittivity

of a homogeneous particle comprising both the shell and the interior of the particle:

where

•

ro and ri (SI unit: m) are the outer and inner radii of the shell, respectively,

•

(dimensionless) is the complex relative permittivity of the particle, and

•

(dimensionless) is the complex relative permittivity of the outer shell.

For this model, the shell parameters for platelets and RBCs are respectively obtained from Ref. 2 and Ref. 3.

The present model is based on a lab-on-a-chip device described in detail in Ref. 1. It consists of two inlets, two outlets, and a separation region in which a nonuniform electric field created by an arrangement of electrodes of alternating polarity alter the particle trajectories. Figure 1 shows the schematic of the modeled geometry. As seen on the figure, the inlet velocity for the lower inlet is significantly higher (853 μm/s) than the upper inlet (154 μm/s) in order to focus all the injected particles toward the upper outlet.

Figure 1: Two dimensional geometry of the modeled device. Details are presented in Ref. 1. The inlet velocity for the bottom inlet is significantly higher than the upper inlet to focus all the injected particles toward the upper outlet (Flow Focusing).

The model uses the following physics interfaces:

•

Creeping Flow to model the fluid flow,

•

Electric Currents to model the electric field in the microchannel, and

•

Particle Tracing for Fluid Flow to compute the trajectories of RBCs and platelets under the influence of drag and dielectrophoretic forces

Three studies are also used:

Study 1 ( and ) solves for the fluid velocity, pressure, and AC electric potential.

Study 2 () estimates the particle trajectories in the flow without the DEP force, so that all particles (platelets and RBC) follow the same path.

Study 3 () computes the particle trajectories including the DEP force.

Results and Discussion

Figure 2 shows the electric potential in the channel. When no dielectrophoretic force is applied, the red blood cells and platelets follow the same path and exit through the same outlet, as shown in Figure 3. When the dielectrophoretic force is applied, the two species are separated due to the differences in their dielectric properties, as shown in Figure 4.

Figure 2: Spatial variation of the electric potential in the microfluidic channel.

Figure 3: Particle trajectories without dielectrophoretic force applied. The RBCs are displayed in red and the platelets in blue. Since the particles are released at the same time and follow a similar path, the platelets are hidden behind the RBCs on the figure.

Figure 4: Particle trajectories with dielectrophoretic force applied. The RBCs are displayed in red and the platelets in blue. For sake of visualization, the relative size of the RBCs has been divided by two.

References

1. N. Piacentini, G. Mernier, R. Tornay, and P. Renaud, “Separation of platelets from other blood cells in continuous-flow by dielectrophoresis field-flow-fractionation,” Biomicrofluidics, vol. 5, 034122, 2011.

2. M. Egger and E. Donath, “Electrorotation measurements of diamide-induced platelet activation changes,” Biophysical Journal, vol. 68, pp. 364–372, 1995.

3. S. Park, Y. Zhang, T.H. Wang, and S. Yang, “Continuous dielectrophoretic bacterial separation and concentration from physiological media of high conductivity,” Supplementary information, Lab on a Chip, vol. 11, pp. 2893–2900, 2011.

Particle_Tracing_Module/Fluid_Flow/dielectrophoretic_separation

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

In the tree, select .

Click .

In the tree, select .

Click .

Click

Geometry 1

Insert the prepared geometry sequence from file. You can read the instructions for creating the geometry in the appendix.

In the toolbar, click

Browse to the model’s Application Libraries folder and double-click the file dielectrophoretic_separation_geom_sequence.mph.

Global Definitions

Parameters 1

Load the model parameters from a file.

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file dielectrophoretic_separation_parameters.txt.

Electric Currents (ec)

Electric Potential 1

In the window, under right-click and choose .

In the window for , locate the section.

In the V0 text field, type 5.

Select Boundaries 8, 17, 26, and 34 only.

Electric Potential 2

In the toolbar, click

and choose .

In the window for , locate the section.

In the V0 text field, type -5.

Select Boundaries 13, 21, and 30 only.

Creeping Flow (spf)

In the window, under click .

Inlet 1

In the toolbar, click

and choose .

Select Boundary 3 only.

In the window for , locate the section.

In the U0 text field, type 134[um/s].

Inlet 2

In the toolbar, click

and choose .

Select Boundary 1 only.

In the window for , locate the section.

In the U0 text field, type 853[um/s].

Outlet 1

In the toolbar, click

and choose .

Select Boundaries 40 and 41 only.

Particle Tracing for Fluid Flow (fpt)

In the window, under click .

In the window for , locate the section.

From the list, choose .

This formulation is chosen because the Lagrangian response time of the particles is about six orders of magnitude smaller than the time for the particles to flow through the channel.

Platelets

In the window, under click .

In the window for , type Platelets in the text field.

Locate the section. From the ρp list, choose . In the associated text field, type rho_p.

In the dp text field, type dp1.

Red Blood Cells

In the toolbar, click

and choose .

In the window for , type Red Blood Cells in the text field.

Locate the section. From the ρp list, choose . In the associated text field, type rho_p.

In the dp text field, type dp2.

Inlet, Platelets

In the toolbar, click

and choose .

In the window for , type Inlet, Platelets in the text field.

Select Boundary 3 only.

Locate the section. In the text field, type range(0,0.01,3).

Locate the section. From the list, choose .

Inlet, Red Blood Cells

Right-click and choose .

In the window for , type Inlet, Red Blood Cells in the text field.

Click to expand the section. From the list, choose .

Outlet 1

In the toolbar, click

and choose .

Select Boundaries 40 and 41 only.

Drag Force 1

In the toolbar, click

and choose .

Select Domain 1 only.

In the window for , locate the section.

From the u list, choose .

Locate the section. Select the check box.

Dielectrophoretic Force, Platelets

In the toolbar, click

and choose .

In the window for , type Dielectrophoretic Force, Platelets in the text field.

Select Domain 1 only.

Locate the section. From the E list, choose .

Locate the section. Select the check box.

From the list, choose .

Shell 1

In the toolbar, click

and choose .

In the window for , locate the section.

In the ts text field, type th_s1.

In the εr,s text field, type epsilon_s1.

In the σs text field, type sigma_s1.

Dielectrophoretic Force, Red Blood Cells

In the window, right-click and choose .

In the window for , type Dielectrophoretic Force, Red Blood Cells in the text field.

Locate the section. From the list, choose .

Shell 1

In the window, expand the node, then click .

In the window for , locate the section.

In the ts text field, type th_s2.

In the εr,s text field, type epsilon_s2.

In the σs text field, type sigma_s2.

Platelets

In the window, click .

In the window for , locate the section.

From the εr,p list, choose . In the associated text field, type epsilon_p1.

From the σp list, choose . In the associated text field, type sigma_p1.

Red Blood Cells

In the window, click .

In the window for , locate the section.

From the εr,p list, choose . In the associated text field, type epsilon_p2.

From the σp list, choose . In the associated text field, type sigma_p2.

Materials

Material 1 (mat1)

In the window, under right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	sigma_f	S/m	Basic
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	epsilon_f	1	Basic
Density	rho	rho_f	kg/m³	Basic
Dynamic viscosity	mu	mu_f	Pa·s	Basic