Numerical simulation of circulating tumor cell separation in a dielectrophoresis based Y-Y shaped microfluidic device

Abstract Efficient and effective separation of circulating tumor cells from biological samples to promote early diagnosis of cancer is important but challenging, especially for non-small cell lung cancer (NSCLC). In this article, a Y-Y shaped microfluidic device was designed to isolate NSCLC cells with a dielectrophoresis approach. Numerical simulations were conducted that the trajectories of cells were traced by solving the electric potential distribution and the flow field in a microchannel. The effects of inlet flow rate ratio of blood sample and buffer on separation performance were studied and optimized by the numerical investigation. Under optimal operating conditions, the separation efficiency can reach around 99%, which is achieved with 100 kHz AC, electrodes potential ranging from 1.6 V to 2.2 V, and flow rate ratio from 1.9 to 2.5. This study presents a potentially efficient, facile and low-cost route for circulating tumor cell separation.


Introduction
Circulating tumor cells (CTCs) are tumor cells shedding from the solid tumor, entering into the bloodstream, surviving in the circulating system, and traveling to distant organs, which resulting in metastasis. The spread of CTCs from initial sites to form distant secondary tumors is one of the main cause of death in cancer patients. [1] CTC detection has received enormous attention because of the potential value in the early diagnosis of cancer, prediction of clinical prognosis, evaluation of therapeutic efficiency, development of targeted drugs and personalized medicine of malignant cancer. Since the concentration of CTCs in the blood is extremely low, on the order of one out of a billion cells, CTCs must be isolated to achieve a high concentration in order to facilitate liquid biopsy efficiently. [2] At present, the technologies commonly used in CTC separation can be categorized as CellSearch system, Nano Velcro CTC chip, microfluidic technology, and other physical separation methods including microfilter and density gradient centrifugation. [3] These methods are classified into positive isolation focusing on CTC capture and negative isolation focusing on capture of leukocytes or erythrocyte. CellSearch system is based on immunomagnetic method which uses magnetic nanoparticles coated with antibodies, aptamers or peptides to capture CTCs and isolate them from blood cells with the impacts of a magnetic field. [4] Although its false negative rate is high and consumes large amounts of blood samples, the standardization of CellSearch makes it the only CTC detection method currently approved by FDA. Nano Velcro CTC chip has a large surface area, which increases the contacting area with CTCs and thus improving the isolation efficiency, while it requires excessive consumption of antibodies. [5] Microfluidic technologies are classified into label-dependent isolation and label-independent isolation. The advantages of Label-independent isolation methods include simple operation process, keeping cell integrity and no need for antibodies. Label-dependent isolation methods commonly use Epithelial cell adhesion molecule (EpCAM) to target CTCs which can improve the specificity of methods. [6] Saliba et al. [7] developed a microfluidic device with antibody functionalized superparamagnetic beads that can self-assemble with magnetic traps in the microchannel.
The capturing efficiency can reach higher than 94%, yet the self-assembled magnetic columns used in these methods are often unstable due to the large hydrodynamic drag force, resulting in low throughput. A magnetic force gradient based microfluidic chip was developed to separate CTCs depending on their expression level of EpCAM. [8] This method is of prognostic value in patients with solid tumors, such as advanced breast, colon, and prostate cancer, while its poor sensitivity for non-small lung cancer (NSCLC) restricts the utilization in treatment. [9] Physical separation methods such as morphology-based microfilter, and density gradient centrifugation methods have advantages of simple operation, maintaining cell integrity and no need for expensive antibodies. However, such methods are limited by the low specificity and high false positive. Among negative isolation methods, magnetic nanobeads coated with anti-CD45 antibodies have been commonly used for separating leukocytes from blood samples, thereby enriching CTCs. [10] Although the recovery rate of this negative method is higher than that of positive method, the purity of isolated CTCs is relatively lower; therefore, further isolation is required. Dielectrophoresis (DEP) microfluidic technologies have been intensively investigated for CTC separation and detection. DEP is one of the most common electrokinetic phenomena and was first described by Pohl. [11] When a nonuniform electric field is applied, it will induce a dipole moment on the particle due to the electrical polarization at the particle's surface. Driven by dielectrophoretic force, the particle has to be migrated in the nonuniform electric field to achieve electrostatic equilibrium. The magnitude of dielectrophoretic force (DEP force) is proportional to the gradient of electric potential, and also depends on the size, deformation and dielectric constant of substance. DEP separations of cells are sensitive to the sizes, shapes, and dielectric properties of the particles, which allows this method to be used widely in bioengineering. In the low frequency region with frequency roughly lower than 10 MHz, the DEP behavior of a cell is largely determined by extracellular factors, including membrane-bound protein, cell size, solution conductivity, and electric permittivity. [12] Becker et al. [13] developed a method to isolate viable cultured breast tumor cells from peripheral blood using DEP method, and succeeded in isolating cultured leukemia cells from blood and cultured breast tumor cells from CD341 hemopoietic stem cells. [14] DEP techniques have been evaluated by scholars to manipulate and sort tumor cells. [15][16] [17][18] However, previous studies used small electrode arrays, limiting the number of cells that can be processed to a maximum of hundreds of thousands. During DEP isolation process, eluate flow rate, and cell loading concentration influenced the efficiency of DEP isolation. The effects of these factors were analyzed and theoretical models were introduced to optimize the design of DEP-based cell separators. [19] Despite of the rapid development of microfluidics-based CTC separation technology, it remains challenging to develop CTC isolation technologies with improved sensibility, specificity and efficiency without compromising the integrity and activity of isolated CTCs.
Besides, the dependence of dielectrophoretic force on the cell size makes cell separation with little difference of dielectric properties a challenge. Primarily, DEP rises from the non-linear interaction applied on an extended dipole body subjected to a nonuniform electric field and surrounded by a dielectric medium, which can be harnessed to move and manipulate microparticles that suspended in liquid media. [20] Correspondingly, the DEP force is the interaction of a nonuniform electric field with the dipole moment it induces (shown in Fig. 1), the magnitude of which is given by [21]

Magnitude of DEP force
where , * is the complex relative permittivity of a specific particle.
The complex permittivity of phase is expressed as where denotes the relative permittivity, denotes the electrical conductivity, and is the angular frequency of the electric field. Previous research has shown that NSCLC are relatively insensitive to some microfluidic isolation methods, which makes their isolation operation difficult. [22] Based on dielectric differences, DEP has great potential to identify and isolate CTCs from other blood cells.

Problem description
In this study, a DEP-assisted microfluidic device is presented and adopted in the isolation of 5 types of NSCLC (HOP-62, HOP-92, NCI-H226, NCI-H23, and EKVX) from blood samples.
As shown in Fig. 2, the cell sorting system consists of low-voltage electrodes and a Y-Y configured microchannel, which is connected with two inlets and two outlets. (the width of inlets and outlets = 50 ) The upper wall of the channel is comprised of successive triangles with alternating sides charged oppositely, which generates a nonuniform electric field in flow region. A blood sample containing erythrocytes (the density = 1050 / 3 , the diameter = 5 , the electric conductivity = 0.31 / , and the relative permittivity = 59) and CTCs (physical properties as Table. 1) is fed into the flow channel from the upper inlet, while a buffer [23] (the density = 1000 / 3 , the dynamic viscosity = 0.001 • , the electric conductivity = 0.055 / , and the relative permittivity = 79) is fed from the lower inlet, which is used to concentrate the cells to accumulate along one side of the channel. After entering the channel, the two streams mix at the intersection of the long channel. When the mixed fluid flow through the channel, due to the effect of the nonuniform electric field, the cells will be subjected to DEP forces with different magnitudes, which are proportional to the sizes of the cells. Since the sizes of CTCs are larger than that of erythrocytes, CTCs will be repelled selectively and captured at the Outlet 2, while other cells will escape from the Outlet 1, thus achieving a cell separation process.

Dielectric properties of CTCs
Gascoyne et al. [24] measured the dielectric properties of NCI-60 panel of tumor cell types and obtained the correlations between the dielectric properties and exterior morphology.
According to their study, there exists a correlation for a spherical mammalian cell when DEP frequency < 1 : where is the medium conductivity, is the capacitance per unit area of the cell plasma membrane, and is the cell crossover frequency, which is proportional to the rate at which the plasma membrane capacitance can be charged in the ionic milieu of the suspending medium in response to an applied electric field. The parameters about CTC properties acquired by them are adopted in this study to conduct numerical simulation in this study. [24]

Governing equations and boundary conditions
In this study, the numerical model is comprised with an electric field and flow field.
According to Eq. (1), the DEP force is generated due to a nonuniform electric field, the intensity of which is given by where represents the electric potential. The electric field distribution is induced by the electric potential of the upper wall, where there is = ± 0 ( 0 is the electric potential exerted on the electrodes).
The flow of fluids in channel is governed by Navier-Stokes equations: where is the mass of a cell; and are the components of the force source , which consists of three terms: where is the drag force term, which is proportional to the relative velocity between the cell and the fluid = − : where is the viscosity of fluid, is the density of particle, and is the mass of particle; is the Brownian force term, which depends on the temperature and the radius of particle : where is a normally distributed random number with a mean of zero and unit standard deviation, = 1.38064852 × 10 −23 / is the Boltzmann constant, ∆ is the time step; [25] and the third term represents the DEP force, which is proportional to the gradient of the electric field. (referring to Eq. 1)

Results and discussion
In this study, the separation performance of the DEP-assisted microfluidic method is      Fig. 7, where it can be seen that the separation of CTC and erythrocytes can be achieved when 1.9 ≤ / ≤ 2.5, 1.6V ≤ 0 ≤ 2.2 , and the sorting efficiency is able to reach approximately 99%.

Conclusions
A novel DEP-based microfluidic strategy was presented in the paper where the cell sorting system is composed of low voltage electrodes and a microchannel in a "Y-Y" configuration.
The mixture of erythrocytes and CTCs are fed into the flow channel from the upper inlet, whilst a carrying fluid is fed from the lower inlet to focus the cells to accumulate along upper side of the channel which features with successive triangles connected with successive alternatively reversed electrodes to induce a non-uniform electric field. When the mixture of cells flows through the long channel, they are subjected to the non-uniform electric field, inducing DEP forces with different magnitudes. Due to the size difference between CTCs and the erythrocytes, DEP force repels CTCs which will be deflected and exit through the lower outlet to achieve effective separation from other cells. The optimal operation conditions were investigated, and high separation efficiency can be obtained with 100kHz AC when electrical potential from 1.6 V to 2.2 V, and inlet flow velocity ratio from 1.9 to 2.5 are applied.

Conflicts of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.