# High-Throughput, Label-Free Isolation of White Blood Cells from Whole Blood Using Parallel Spiral Microchannels with U-Shaped Cross-Section

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{p}/D

_{h}~ 0.1 (where a

_{p}is particle diameter and D

_{h}is hydraulic diameter of the channel) align in four equilibrium positions where shear gradient lift force and wall induced lift force balance each other [27]. According to recent studies, in a spiral microchannel, particles are focused in one single equilibrium position close to the inner wall of the microchannel while smaller sized particles continue to recirculate by the effect of the secondary Dean flow [16,28].

## 2. Design Principle

_{p}is the particle diameter. The magnitude of ${C}_{L}$, thus, ${F}_{L}$ starts from zero in the channel centerline reaches a maximum value, and then goes back to zero again around 0.2${D}_{h}$ away from the channel wall, which is considered as the equilibrium position of particles [41]. Beyond this distance, ${C}_{L}$ becomes negative in sign showing the dominant effect of wall-induced lift force and further increases in magnitude by moving toward the walls [27].

_{L}/F

_{D}) is proportional to ${a}_{p}{}^{3}$, therefore, as particles become larger, the inertial lift force exerting on them becomes greater than the Dean drag force and vice versa for small particles. Hence, in a spiral microchannel, larger particles tend to stay in equilibrium positions near the microchannel inner wall, while smaller ones are constantly circulated by the secondary flow.

## 3. Materials and Methods

#### 3.1. Device Fabrication

#### 3.2. Numerical Simulation

^{®}software.

^{−14}N and 1 × 10

^{−20}N·m, respectively, hence, to be considered as a steady-state condition for the particle. Once convergence occurs, calculations will start over with the particle being placed at another location in the yz-plane. The following formulas are used to update the velocities:

#### 3.3. Mesh Independency

_{p}, 0.1 × D

_{p}, and 0.05 × D

_{p}, respectively (Figure 3B), in order to preserve less than 0.1% change in the y-component of the lift force with D

_{p}being the particle diameter.

#### 3.4. Sample Preparation

#### 3.5. Experimental Approach

## 4. Results and Discussion

#### 4.1. Device Design for Cell Separation

#### 4.2. Validation of the Numerical Simulations

#### 4.3. Simulation of the Secondary Flow in the Spiral Microchannel

#### 4.4. Presence of the Secondary Flow in the Spiral Microchip

#### 4.5. The Effect of the Flow Rate

#### 4.6. The Effect of Hematocrit

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**A**) The 4-loop parallel spiral microchannels fabricated in PDMS with the corresponding mold preview. (

**i**) The magnified view of section (

**i**). (

**ii**) The magnified view of section (

**ii**). (

**B**) Schematic of the cross-section of the spiral microchannel (The dimensions are in µm).

**Figure 2.**Flowchart of the numerical algorithm used in this study for the calculation of the forces acting on particles. The original algorithm was proposed to investigate particle inertial migration in a straight microchannel [31]. It was later modified to be used in a rectangular spiral microchannel [32]. We extended the original algorithm to run support the corresponding calculations of any other desired spiral microchannel cross-sections.

**Figure 3.**Illustration of the mesh in the fluid domain. (

**A**) The domain was separated into two zones in which tetrahedral mesh was used between the particle surface and the microchannel walls with a maximum size of 0.1 × D

_{p,}and the structured mesh was used outside the block, including the particle. (

**B**) Triangular mesh was used on the surface of the particle with a maximum size of 0.05 × D

_{p}.

**Figure 4.**(

**A**) 3D schematic of the proposed spiral microchip in this study. The design includes two parallel U-shaped cross-section spiral microchannels that consist of: (I) two inner inlets for the injection of blood samples, (II) two outer inlets for the injection of sheath fluid, (III) shared outer outlet for the extraction of RBCs and platelets, and (IV) shared inner outlet for the extraction of WBCs. (

**B**) Larger blood cells, i.e., WBCs, affected by dominant inertial forces are focused along the inner microchannel wall. In comparison, smaller blood cells, i.e., RBCs and platelets, are forced to migrate toward the outer microchannel section by the effect of the secondary flow (flow direction is shown in green arrows), which in turn stops the smaller cells from getting back to the inner microchannel section. (

**C**) The overall process of WBC sorting and enumeration. Blood cell count is done using a Neubauer chamber, and the resulting WBC isolation efficiency is calculated using the fractional ratio of blood cells in specific outlets to the total count of blood cells in both outlets.

**Figure 5.**(

**A**) Calculated inertial force in a straight channel at z = 0 using the algorithm in the present study versus inertial force reported by Ref. [31]. (

**B**) Calculated inertial force field acting on a 10 µm particle in the present study.

**Figure 6.**Calculated secondary flow streamlines and velocity vectors in the second loop of the designed spiral microchannel cross-section at x = 0. Velocity vectors are being directed from the inner wall to the outer wall in the middle passway with: (

**A**) 2 mL/min, (

**B**) 3 mL/min inlet flow rate (Note that in this figure the origin of y-direction lies on the origin of the spiral microchannel).

**Figure 7.**(

**A**) Contour of velocity magnitude in the spiral microchannel at the second loop at x = 0 with an inlet flow rate of 3 mL/min. (

**B**) Velocity magnitude profile with the change in inlet flow rates at z = 40 µm (z = 0 indicates the bottom wall of the microchannel and y = 0 indicates the centerline of the microchannel cross-section (cl), this difference in the maximum velocity magnitude results in the streamlines being directed from the inner microchannel wall (iw) toward the outer microchannel wall (ow). (

**C**) The calculated inertial force field acting on a 10 µm particle in the inner section of the spiral microchannel with an inlet flow rate of 5 mL/min. Equilibrium positions are shown as blue dashed lines in the microchannel cross-section. (

**D**) The inertial force applying to a 10 µm particle alongside y-direction at z = 64.4 µm (z/200 µm = 0.322) and z = 82.2 µm (z/200 µm = 0.411). As can be seen, the inertial force at the beginning of the passway is much lower than the wall-induced inertial force. The Dean drag force can overcome this inertial force, therefore, allowing the particles smaller than 10 µm to move toward the outer section of the spiral microchannel.

**Figure 8.**Schematic of (

**A**) the critical location for a 14 µm particle in terms of experiencing the maximum shear stress throughout the spiral microchannel, (

**B**) the total shear stress exerting on the particle in the x-direction, (

**C**) the total shear stress exerting on the particle in the y-direction, (

**D**) the total shear stress exerting on the particle in the z-direction, (

**E**) the total magnitude of shear stress exerting on the particle. The resulting maximum stress in the x, y, and z-direction was found to be 35 Pa, 35 Pa, and 20 Pa, respectively. Moreover, the maximum value for the magnitude of total shear stress is 45 Pa.

**Figure 9.**Images of the left side spiral at (

**A**) Inlets, (

**B**) outlets showing the effect of the secondary flow on mixing the colored fluid throughout the entire microchannel. The colored fluid and DI water were pumped through the microchannel from the inner and outer inlets, respectively.

**Figure 10.**The effect of the sample inlet flow rate on the removing ratio of (

**A**) RBCs, (

**B**) platelets for 1% blood hematocrit sample. RBC removing ratio is the most sensitive to changes in inlet flow rate with a maximum value at 6 mL/min. The removing ratio of platelets is the least dependent on the flow rate and they can be extracted from the shared outer outlets with high removing ratios.

**Figure 11.**The effect of the sample inlet flow rate on WBC: (

**A**) isolation efficiency, and (

**B**) purity for a 1% blood hematocrit sample. The WBC isolation efficiency experiences a massive drop in higher flow rates due to the existence of high-strength dean vortices which force the WBCs to migrate to the outer microchannel wall. The outlet samples are the purest with flow rates of 4, 5, and 6 mL/min. The higher the removing ratio of RBCs and platelets, the higher WBC purity.

**Figure 12.**The effect of blood hematocrit on the removing ratio of (

**A**) RBC, (

**B**) Platelets. The removing ratio mainly decreases with an increase in blood hematocrit due to a rise in the effect of cell-cell interaction. While RBC removing ratio is highly dependent on blood hematocrit, the removing ratio of platelets does not seem to change very much with a change in blood hematocrit.

**Figure 13.**The effect of blood hematocrit on WBCs’: (

**A**) isolation efficiency, (

**B**) purity. Separation efficiency mainly decreases with an increase in blood hematocrit due to the rise in the effect of cell-cell interaction in higher flow rates. Sample purities for lower hematocrits are mainly higher since to amount of RBCs in the diluted sample is lower. WBC purity is higher at the inlet flow rates of 5, 6, and 7 mL/min due to an increase in RBCs removing ratio.

**Figure 14.**Illustration of the flow in outlet bifurcation in the left spiral for 1% hematocrit blood sample with (

**A**) 2 mL/min (

**B**) 4 mL/min (

**C**) 6 mL/min and (

**D**) 7 mL/min flow rates and collected blood samples with (

**E**) 1%, (

**F**) 2% and (

**G**) 5% hematocrit for 6 mL/min flow rate from microchip’s: (I) outer outlets and (II) inner outlets. As can be seen, for constant sample hematocrit, increasing the flow rate reduces the concentration of RBCs in the inner outlets, which results in an increase in WBC WBC and isolation efficiency and RBC removing ratio. For constant flow rates, reducing the sample hematocrit (i.e., higher dilution factors) further reduces the concentration of RBCs in the inner outlets, thus, the collected sample from the inner outlet looks more transparent in comparison to higher sample hematocrits.

**Table 1.**The microchip’s specifications in terms of sample flow rate, microchannel Reynolds number, and Dean number.

Sample Flow Rate (mL/min) | Sample Flow Rate Per Spiral (mL/min) | Re | De |
---|---|---|---|

2 | 1 | 32.68 | 4.50 |

3 | 1.5 | 49.02 | 6.75 |

4 | 2 | 63.36 | 9.00 |

5 | 2.5 | 81.70 | 7.47 |

6 | 3 | 98.04 | 13.50 |

7 | 3.5 | 114.38 | 15.75 |

8 | 4 | 130.72 | 18.00 |

**Table 2.**Summary of the spiral microchip best performance results in the isolation of WBC, RBC, and Platelets based on the inlet sample flow rate and hematocrit.

Sample Hematocrit | ||||
---|---|---|---|---|

1% | 2% | 5% | ||

Flow rate (mL/min) | 6 | 5 | 4 | |

WBC | Purity (%) | 88.3 | 74.8 | 61.5 |

Isolation efficiency (%) | 95.3 | 92.5 | 88.8 | |

RBC | Removing ratio (%) | 95.7 | 88.4 | 82.5 |

Platelet | Removing ratio (%) | 94.2 | 93.8 | 91.6 |

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**MDPI and ACS Style**

Mehran, A.; Rostami, P.; Saidi, M.S.; Firoozabadi, B.; Kashaninejad, N.
High-Throughput, Label-Free Isolation of White Blood Cells from Whole Blood Using Parallel Spiral Microchannels with U-Shaped Cross-Section. *Biosensors* **2021**, *11*, 406.
https://doi.org/10.3390/bios11110406

**AMA Style**

Mehran A, Rostami P, Saidi MS, Firoozabadi B, Kashaninejad N.
High-Throughput, Label-Free Isolation of White Blood Cells from Whole Blood Using Parallel Spiral Microchannels with U-Shaped Cross-Section. *Biosensors*. 2021; 11(11):406.
https://doi.org/10.3390/bios11110406

**Chicago/Turabian Style**

Mehran, Amirhossein, Peyman Rostami, Mohammad Said Saidi, Bahar Firoozabadi, and Navid Kashaninejad.
2021. "High-Throughput, Label-Free Isolation of White Blood Cells from Whole Blood Using Parallel Spiral Microchannels with U-Shaped Cross-Section" *Biosensors* 11, no. 11: 406.
https://doi.org/10.3390/bios11110406