# Design and Simulation of an Integrated Centrifugal Microfluidic Device for CTCs Separation and Cell Lysis

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{8}cells/min. Che et al. [34] proposed a high-throughput vortex chip with contraction–expansion channel arrays to separate CTCs by employing several parallelized channels and reservoirs to increase the population of rare CTCs with rapid flow rate (0.8 mL/min), high efficiency (83%), and high purity. For serpentine inertial device applications, Zhang et al. [37] presented a device to separate blood cells from plasma. Straight channels were also used in some methods of CTC separation [42,43]. More examples for inertial methods and other size-based separation methods of CTCs are reviewed by Hao et al. [44].

## 2. Materials and Methods

#### 2.1. Description of the Proposed Platform Geometry and Function of Each Part

#### 2.2. Governing Equations of Fluid Flow

_{m}is the average fluid flow velocity and D

_{h}is the characteristic length or hydraulic diameter of the channel that can be determined by equation (4), in which H and W are height and width of the channel, respectively.

#### 2.3. Governing Equations for Particle Tracking

_{p}), Reynolds number ($R{e}_{C}$), and lateral positions in the channel cross-section (z) [52,53]. Moreover, the creation of secondary flow (Dean flow) as two counter-rotating vortices within contraction sections of this channel leads to exerting a drag force on the particles (F

_{D}), called Dean drag force that is presented in Equation (11). ${U}_{Dean}$ in this equation is the strength (velocity) of secondary flow. The balance between F

_{L}and F

_{D}forces in the mentioned channels determines the equilibrium positions of the cells for cell sorting [15].

_{p}is the diameter of a particle, and ${f}_{L}$ expresses the inertial lift force coefficient, which is related to the channel Reynolds number and the particle position along the channel cross-section (z).

_{1}and C

_{2}are correction coefficients that are obtained by using DNS simulation [56] that can be used for wide range of Reynolds numbers and aspect ratios (AR = W/H) of the channel, as shown in Table 1.

_{max}, H, and d

_{p}. H is the distance between walls, U

_{max}is the maximum channel velocity, and G

_{1}and G

_{2}are functions of nondimensional wall distance s. These functions are plotted in Figure 2. s is the nondimensionalized distance from the particle to the reference wall; the actual distance divided by H, so that 0 < s < 1 for particles in channel. The β and $\mathsf{\gamma}$ are normalized by U

_{max}and H. The main characteristics of the formula remain unchanged unless Re is much higher than 100, which is rare in inertial microfluidics so it can be used for a wide range of Reynolds numbers [56].

^{3}) is higher than the density of the carrier fluid (1000 kg/m

^{3}) and in the first terms in Equations (15) and (16) in the first parentheses, the magnitude of $\left({\rho}_{p}-{\rho}_{f}\right)H$ and ${\rho}_{f}{d}_{p}$ are in the same order of magnitude because, although ${\rho}_{f}>{\rho}_{p}-{\rho}_{f}$ in the other side, the height of the channel is several times greater than particle diameters $\left({d}_{p}<H\right)$. Therefore, the numerator and denominator in this parenthesis are in same order of magnitude. Moreover, the velocity of a rotating object at radial distance r is equal to $r\omega $ and, since the fluid velocity originates from the rotation of the platform, it can be estimated that ${U}_{\mathrm{max}}\sim {v}_{p}\sim r\omega $. The following equations show that, for instance, at an angular velocity of 1000 rpm (~100 rad/s) and higher than this value, which is common for LOCD devices, each term in the numerator and denominator for second parentheses in Equations (15) and (16) are almost in the same order of magnitude. The same comparison can work for the third parenthesis. In summary, it can be concluded that, in our proposed application, the effect of centrifugal and Coriolis forces in particle motion has notable importance as does inertial lift force.

#### 2.4. Governing Equations for Mixing

#### 2.5. Numerical Method

^{3}. Centrifugal and Coriolis forces were considered as body forces due to the rotation of the system, and inertial lift forces were applied as dominant forces for lateral migration of particles. The proposed geometry for the separation unit is shown in Figure 1C. In this unit, it was assumed that the flow is 3D, and particle–particle interactions were neglected due to the dilution of blood samples in the inertial method in practical applications. The simulations were performed for different angular velocities ranging from 500 rpm to 3000 rpm. The particles contained by the fluid (blood sample) entered from the inlet and passed through the contraction–expansion array. Based on the lift, drag, centrifugal, and Coriolis forces applied, the particles were sorted, based on their size, into different outlets. By using the appropriate boundary conditions and generating a proper mesh for the proposed separation geometry, the simulations were performed for different angular velocity.

^{3}for inlet 1, the entrance of the fluids (plasma) with isolated CTCs, and 1 mole/m

^{3}for inlet 2 for the entrance of the lysis buffer, the concentration equation was solved. For the walls of the microchannel, the no-slip condition was used for the fluid flow study and properties of water, including 1000 kg/m

^{3}for density, 0.001 Pa.s for viscosity, were used. The no-mass flux boundary condition was considered for all walls of the microchannel and diffusivity of $1.67\times {10}^{-9}{\mathrm{m}}^{2}/\mathrm{s}$ was considered for mass transport studies.

## 3. Results and Discussion

^{3}; polystyrene particles with diameters of 5 µm and density of 1.05 g/cm

^{3}; silica particles with a diameter of 5 µm and density of 2.0 g/cm

^{3}. After passing through the narrow region of the channel, these particles were sorted by applied centrifugal force as well as wall-induced lift forces and followed distinct streamlines to specified downstream outlets. The authors reported that, at an angular velocity of 750 rpm, 98% of silica particles left the channel through outlet number 5 and about 87% of polystyrene particles with a diameter of 3 µm left the channel from outlets 9–11. In their experiments, about 80% of polystyrene particles with diameters of 5 µm were collected in outlets 9 and 10. Our simulations for particle trajectories are shown in Figure 3C and Figure 3D and our results agree with their experimental data, predicting that larger particles go through outlet 5 and particles with a diameter of 3 µm and 5 µm with lower densities leave the channel through outlets 9, 10, and 11.

## 4. Limitations and Suggestions

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Proposed LOCD device. (

**A**) Two-dimensional schematic of the designed centrifugal-based microfluidic biochip composed of serially arranged separator and mixer subunits. (

**B**) Magnified view of the proposed device. (

**C**) Cell separation unit, the CTCs are separated from the WBC cells by the implementation of inertial contraction–expansion arrays. (

**D**) The mixer unit for cell lysis: (I) serpentine channel without obstacles and (II) with obstacles.

**Figure 3.**(

**A**) An illustration of the Morijiri et al. [38] model, (

**B**) Numerical simulation results for the velocity field in narrow region. (

**C**,

**D**) particles’ paths for different particles at different sections of the platform.

**Figure 4.**Simulation of Flow field for the proposed cell separation unit (

**A**) formation of two counter-rotating vortices in a cross-section in the contraction region. (

**B**) Defined vertical line in the cross-section. (

**C**) Radial velocity profile for the different angular velocity of disk. (

**D**) Mesh independency analysis for cell separation unit at three different mesh densities for lateral fluid velocity magnitude along the vertical red line in the middle of the channel cross-section. (

**E**) Lift force magnitude distribution and its vectors in a cross-section of contraction section for 20 µm particles. (

**F**) Lift force magnitude distribution and its vectors in a cross-section of expansion section for 20 µm particles.

**Figure 5.**Particle tracking in proposed separation unit for different angular velocity. (

**A**–

**F**) Particles’ path lines and location at the outlets of the channel for different angular velocity. (

**A**) 500 rpm, (

**B**) 1000 rpm, (

**C**) 1500 rpm, (

**D**) 2000 rpm, (

**E**) 2500 rpm, (

**F**) 3000 rpm. Red lines show the path lines for CTCs and blue lines show the path lines for WBCs. (

**G**) Separation efficiency for different angular velocity. (

**H**) Path lines for CTCs with 15 and 20 µm diameters and WBCs with a 10 µm diameter.

**Figure 6.**Validation of the mixing unit for our simulation method vs. La et al.’s experiment. (

**A**) Concentration contour for the simulation model. (

**B**) Comparison of mixing quality at different down-channel locations between numerical and experimental model.

**Figure 7.**Mixer unit simulation. (

**A**) Mixing pattern for serpentine micromixer without obstacles. (

**B**) Vortex formation in serpentine channel without obstacles. (

**C**) Velocity distribution for micromixer with obstacles at 2000 rpm. (

**D**) Vortex formation in a serpentine channel with obstacles and related lateral velocity distribution within the cross-section. (

**E**) Mixing pattern in proposed micromixer with obstacles at 2000 rpm. (

**F**) Mixing pattern in the proposed micromixer in different cross-sections along the channel.

**Figure 8.**(

**A**) Mesh independency analysis for mixer unit. (

**B**) Mixing quality assessment along the down-channel length. (

**C**) Mixing quality at different angular velocities.

**Table 1.**Correction coefficients for inertial lift force proposed by Liu et al. [56].

AR | C_{1} | C_{2} |
---|---|---|

1 | 0.056 | 0.03 |

2 | 0.021 | 0.018 |

4 | 0.023 | 0.127 |

6 | 0.068 | 0.135 |

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**MDPI and ACS Style**

Nasiri, R.; Shamloo, A.; Akbari, J.; Tebon, P.; R. Dokmeci, M.; Ahadian, S.
Design and Simulation of an Integrated Centrifugal Microfluidic Device for CTCs Separation and Cell Lysis. *Micromachines* **2020**, *11*, 699.
https://doi.org/10.3390/mi11070699

**AMA Style**

Nasiri R, Shamloo A, Akbari J, Tebon P, R. Dokmeci M, Ahadian S.
Design and Simulation of an Integrated Centrifugal Microfluidic Device for CTCs Separation and Cell Lysis. *Micromachines*. 2020; 11(7):699.
https://doi.org/10.3390/mi11070699

**Chicago/Turabian Style**

Nasiri, Rohollah, Amir Shamloo, Javad Akbari, Peyton Tebon, Mehmet R. Dokmeci, and Samad Ahadian.
2020. "Design and Simulation of an Integrated Centrifugal Microfluidic Device for CTCs Separation and Cell Lysis" *Micromachines* 11, no. 7: 699.
https://doi.org/10.3390/mi11070699