Microfluidic-based single cell trapping using a combination of

Acta Mech. Sin. (2016) 32(3):422–429 DOI 10.1007/s10409-016-0558-2

RESEARCH PAPER

Microfluidic-based single cell trapping using a combination of stagnation point flow and physical barrier Miao Yu1 · Zongzheng Chen1 · Cheng Xiang2 · Bo Liu1 · Handi Xie3 · Kairong Qin1

Received: 29 September 2015 / Revised: 24 December 2015 / Accepted: 29 December 2015 / Published online: 25 March 2016 © The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2016

Abstract Single cell trapping in vitro by microfluidic device is an emerging approach for the study of the relationship between single cells and their dynamic biochemical microenvironments. In this paper, a hydrodynamic-based microfluidic device for single cell trapping is designed using a combination of stagnation point flow and physical barrier. The microfluidic device overcomes the weakness of the traditional ones, which have been only based upon either stagnation point flows or physical barriers, and can conveniently load dynamic biochemical signals to the trapped cell. In addition, it can connect with a programmable syringe pump and a microscope to constitute an integrated experimental system. It is experimentally verified that the microfluidic system can trap single cells in vitro even under flow disturbance and conveniently load biochemical signals to the trapped cell. The designed micro-device would provide a simple yet effective experimental platform for further study of the interactions between single cells and their microenvironments.

Miao Yu and Zongzheng Chen contributed equally to this work. Electronic supplementary material The online version of this article (doi:10.1007/s10409-016-0558-2) contains supplementary material, which is available to authorized users.

B

Kairong Qin [email protected]

1

Department of Biomedical Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China

2

Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore

3

Western Reserve Academy, Hudson, OH 44236, USA

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Keywords Single cell trapping · Microfluidics · Stagnation point flow · Physical barrier · Hydrodynamic tweezers · Dynamic biochemical signal

1 Introduction Currently, single-cell analysis, especially the interaction between a single cell and microenvironment, which involves a large variety of biophysical (such as shear stress) and biochemical (such as Adenosine Triphosphate (ATP)) factors with dynamical change, has gradually become a biological research hotspot and plays a significant role in embryonic development, tissue repair, drug screening of serious diseases, as well as physiological and pathological cell studies [1,2]. Single cell trapping is the first critical step for single-cell analysis. Up to now, microfluidics has become a popular and efficient experimental platform for single cell trapping with its unique superiority in cellular analysis compared to traditional analysis methods [3–5]. During the past several years, a number of techniques have been proposed for trapping single cells in microfluidic chips, which include optical tweezers [6,7], dielectrophoresis trapping [8,9], magnetic trapping [10], acoustics trapping [11,12], and hydrodynamic tweezers [13–21]. These methods have been used to explore some physical and biological problems, but each has its own limitations. The first hydrodynamic-based particle manipulation was proposed by Taylor [13] using the principle of stagnation point flow in 1934. Afterwards, this groundbreaking device has been improved and gradually applied to the single cell trapping in microfluidic chips [14–21]. At present, two categories of microfluidic-based hydrodynamic tweezers, i.e.

Microfluidic-based single cell trapping using a combination of stagnation point flow and physical barrier

the contact-type and the non-contact-type, have been developed. The contact-type tweezers use physical barriers to immobilize cells or particles through the fluid flow [15,16]. Generally, these methods can trap a large number of single cells by serial or collateral arrays with high efficiency. But mostly, they are not easy to load external dynamic biochemical signals quantitatively and accurately to stimulate the trapped cells due to the special channel barriers in the contact-type tweezers and the filtering characteristics of micro-channels [22]. On the other hand, the non-contacttype tweezers mostly rely on the stagnation point flows [18,19] or steady streaming microeddies and microvortices [20,21]. Basically, the tweezers were able to manipulate single cells with fine-scale [18] and had the ability to transport biochemical signals to the trapped cells, but they were unstable during the trapping process, which leads to difficulty in quantitatively analyzing the loading signals. The introduction of an external controller may improve the stability, but it needs to add complex and expensive optical sensors and control systems [19]. In addition, trapping via microeddies or microvortices was also not simple because of the requirements for magnets or oscillators [20,21]. To overcome the shortcomings in the hydrodynamic tweezers using either physical barriers (contact-type tweezers) or stagnation point flow (non-contact-type tweezers), a microfluidic-based hydrodynamic device for single cell trapping together with dynamic biochemical signal loading is to be designed using a combination of both stagnation point flow and physical barrier. The designed hydrodynamic microfluidic device connects with several syringe pumps, and an inverted microscope to constitute an integrated system. It will be experimentally verified by the integrated system whether the microfluidic device can trap single cells in vitro and conveniently load biochemical signals to the cells.

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2 Materials and methods 2.1 A microfluidic channel as part of a stagnation flow field In a shallow microfluidic channel, which has a high aspect ratio (width to height), it is assumed that a fully developed viscous, incompressible, steady laminar flow is driven by pressure gradient ∇ p. Because of the high aspect ratio, the sidewall effect of viscous flow is negligible. Therefore, the height-averaging velocity V¯ = V¯ (r, θ ) in polar coordinate (the origin is in the middle along the z-axis) is expressed as [23] 2

H ∇ p, V¯ (r, θ ) = − 12η

(1)

where η is the fluid viscosity, H is the height of the channel. By introducing the complex potential W (Z) = ϕ (r, θ ) + jψ (r, θ ) = AZ n (Z = r ejθ , A is√a real number, n is a positive number greater than 1, j = (−1)) in the Z-plane, the height-averaging velocity V¯ (r, θ ) can be expressed by the potential function ϕ (r, θ ) or the stream function ψ (r, θ ) [24] 1 ∂ϕ 1 ∂ψ ∂ψ ∂ϕ er + eθ = er − eθ V¯ (r, θ ) = ∂r r ∂θ r ∂θ ∂r = Anr n−1 [cos (nθ ) er − sin (nθ ) eθ ] ,

(2)

where er and eθ are the base vectors in polar coordinate. Following Qin and his co-workers [24], the equipotential lines and flow lines can be determined by letting the potential function and the stream function be equal to constants. Figure 1a shows the distribution of the equipotential lines (dashed) and the flow lines (solid) when n is 2.5. At the origin of coordinates, the height-averaging velocity V¯ (r, θ ) is zero, i.e. the origin is a fluid stagnation point.

Fig. 1 (Color online) Design of the trapping chamber. a Construction of the trapping chamber in the flow field (n = 2.5). b Illustration of the red box in a. Line AB is the curved boundary, BC and CO are the straight boundaries

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Let us construct a shallow microfluidic chamber with a stagnation point (see the dark part in Fig. 1a). Its axis coincides with the x-axis, the upper and lower curved boundaries coincide with two symmetric flow lines. Then the equations of the upper and lower curved boundaries can be introduced and satisfy [24] r n sin (nθ ) = r0n sin (nθ0 )

(θ ∈ [θ0 , π −θ1 ]) ,

(3)

and r n sin (nθ ) = −r0n sin (nθ0 )

(θ ∈ [θ1 − π, −θ0 ]) ,

(4)

respectively, where θ1 is the supplementary angle of the polar angle of the upper curved boundary and is equal to 43 π when n is 2.5. θ0 and r0 are the angle and radius at the starting point of the upper boundary of the flow chamber in (x, y) plane, respectively, and are expressed as θ0 ≈ tan−1

W 2L

(5)

and  r0 =

L2 +

W2 , 4

(6)

where L is the total length of the shallow microfluidic channel, and W is the width of the chamber inlet. In addition, the upper and lower straight boundaries follow θ =±

π n

   L r ∈ 0, . 2

(7)

The entire shallow microfluidic chamber is constructed with the upper and lower curved boundaries and straight boundaries, where the cross-point of the curved boundary and straight boundary is located at the flow line. The white dashdotted lines in Fig. 1b are two equipotential lines through the origin, whose angle satisfy

θ =±

π 2n

   r ∈ 0, r0 n sin (nθ0 ) .

For this shallow microfluidic chamber, the heightaveraging velocity along the central axis x is expressed as [24] | V¯ (r, 0) | =

Qnr n−1 . 2Hr0n sin (nθ0 )

(9)

2.2 A combination of stagnation point flow and physical barrier It can be clearly seen from Eq. (9) that along the central axis (θ = 0), as r decreases, the average velocity decreases gradually from the maximum to zero at the origin. Thus, when a cell flows along the central axis and reaches the origin (trapping point), its flow velocity is zero theoretically. In practice, however, cells cannot easily reach the trapping point due to the sidewall effects by fluid viscosity around the origin. Thus, a resistance channel and two output channels are designed as shown in Fig. 2, which allow a cell easily to reach the cell trapping point and prevent it from escaping from the point. More specifically, it is assumed that the total flow rate of the flow into the chamber is Q, and the flow rates flow out through the upper output channel, the lower output channel and the resistance channel are Q 1 , Q 2 , and Q 0 , respectively; therefore, Q = Q1 + Q0 + Q2.

(10)

Accordingly, the pressure difference P between the fluid stagnation point and the outlet of micro-channel system satisfies Q 1 R1 = Q 0 R0 = Q 2 R2 = P,

(11)

where R1 , R2 , and R0 are the flow resistances of the upper and lower output channel, and the resistance channel respectively. And R0 is greater than R1 and R2 .

Fig. 2 Capture mechanism. a Schematic of the automatic trapping system. b The equivalent principle diagram for the system

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(8)

Microfluidic-based single cell trapping using a combination of stagnation point flow and physical barrier

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Fig. 3 Design of the PDMS-glass microfluidic chip. The detailed descriptions of the device are as follows: A cell trapping chamber, B microchannel system for automatic cell trapping, 1 medium inlet, 2 cell suspension or fluorescent solution inlet, 3 upper medium inlet channel, 4 lower medium inlet channel, 5 cell suspension inlet channel, 6 upper curved boundary, 7 lower curved boundary, 8 upper straight boundary, 9 lower straight boundary, 10 upper outlet channel, 11 lower outlet channel, 12 resistance channel, 13 output channel, 14 fluid outlet

It is obvious in Eq. (11) that there is an inverse relationship between the flow rate and the resistance. When a cell reaches the trapping point along the central flow line, it will nearly block the resistance channel as its size is larger than the inlet of resistance channel. Thus, R0 will increase, and Q 0 will decrease. Correspondingly, Q 1 and Q 2 will increase in order to ensure the conservation of flow according to Eq. (10), i.e. other cells will flow out through the upper and lower output channels to ensure a single-cell trapping. On the other hand, when the flow field in the chamber is affected by flow disturbance or flow rate changes, the trapped cell will move away from the trapping point. Then the resistance channel reopens, Q 0 will increase soon and pull the cell back to the trapping point, so it can achieve a stable trapping. 2.3 Generation of dynamic biochemical signals In order to study the interaction between the single cell and the microenvironment, especially the response to the dynamic biochemical signals, the experimental equipment for generating dynamic biochemical signals is made from two syringe pumps and two injectors filling with the solute and solvent, respectively. The two injectors are connected to a T-bend by silicone tubes to generate a dynamic biochemical signal by controlling the flow rates of the solute and solvent, respectively. Suppose that Q A1 , Q A2 , and Q A are the flow rates of solute A, solvent A, and solution A respectively, and φA1 and φA are the concentrations of solute A and solution A, the mass conservation law leads to Q A1 + Q A2 = Q A , Q A1 φA1 = Q A φA ,

(12)

Q A φA , φA1

Q A2

  φA . = QA 1 − φA1

(14)

From Eqs. (13) and (14), a desired biochemical signal with flow rate Q A and concentration φA can be implemented controlling the syringe pumps by setting the flow rates Q A1 and Q A2 of injectors filled with solute A and solvent A, respectively.

2.4 Device design and fabrication In the hydrodynamic trap, a polydimethylsiloxane-glass (PDMS-glass) microfluidic device is designed as shown in Fig. 3. The transverse width for the inlet of shallow microfluidic channel W is about 50 μm, and the longitudinal length of the chamber L is 1 mm. Considering the cell size is about 10–12 μm, the width of the resistance channel 12 (shown in Fig. 3) Wr , is designed to be 5 μm and the heights of micro-channels and chambers H are all about 30 μm. All the micro-channels were patterned in PDMS (Sylgard 184, DOW CORNING) by replica molding. The mold was prepared by spin coating a thin layer of negative photoresist (SU-8, MicroChem) onto a single side polishing silicon wafers and patterned with UV exposure. Next, the micro-channel layer was obtained by pouring PDMS with 10:1(w/w) base: crosslinker ratio onto the mold yielding a thickness of 3 mm roughly. After curing the elastomer for 2 h at 80 ◦ C, the PDMS slab was peeled from the mold, punched, and hermetically bonded to a coverslip by plasma oxidation. 2.5 Implementation of integration system

and then Q A1 , Q A2 can be expressed as Q A1 =

and

(13)

The fabricated microfluidic chip is connected with a syringe pump (NE-1000, NEW ERA, USA), an inverted microscope

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Fig. 4 a The schematic diagram and b actual construction of the integrated experimental system. The detailed descriptions of this system are as follows: 15 fluid driving system, 16 display system, 17 inverted microscope, 18 microfluidic chip, 19 cell suspension, 20 fluorescent solution, 21 materials importing tube, 22 medium importing tube, 23 waste

(CKX41, OLYMPUS, Japan) equipped with a charge coupled device (CCD) camera (DS126431, CANON, Japan), which forms the trapping system for single cell culture in vitro. The fluid driving system 15 (shown in Fig. 4) consists of syringe pumps and several injectors, where the injectors are driven by the syringe pumps in order to control the flow rate and velocity when fluid is injected into the micro-channels. In particular, when doing the trapping experiments, the importing tube 21 is connected to the injector containing the cell suspension 19, and then it turns to connect the fluorescent solution 20 while loading dynamic biochemical signals into the chamber. Here, the fluorescent solution 20 is generated by the biochemical signal generator. Another injector is always filled with medium 22. After setting velocity and flow rate, the medium and cell suspension (or fluorescent solution) are injected into the chip from inlet 1 and inlet 2 , respectively. And the images observed through the objective area of the inverted microscope can be real-time displayed on the connected CCD camera (Fig. 4). 2.6 Cell suspension and fluorescent solution preparation The HEK293T cell line was purchased from the American Type Culture Collection (ATCC, Manassas, VA, USA). Dulbecco’s Modified Eagle Medium (DMEM/high glucose), fetal bovine serum (FBS), phosphate buffered saline (PBS), trypsin–EDTA, and penicillin/streptomycin were provided by Hyclone (Thermo Scientific, USA). The HEK293T cell line was cultured in standard tissue culture flasks using Dulbecco’s Modified Eagle Medium supplemented with 10 %

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FBS, 2 % penicillin / streptomycin and 1 % l-glutamine (Sigma). After the third generation, the cells were collected via trypsin, and then a cell suspension at a density of 106 cells/mL was made. In addition, rhodamine-6 (Sigma) was dissolved in water with a concentration of 10 μmol/ml. 2.7 Experimental protocol To demonstrate proof-of-principle of the hydrodynamic microfluidic device, HEK293T cells were injected into this PDMS-glass microfluidic channel. After 293T cells entered the trapping chamber through inlet 2, turned on the medium inlet 1, and made its flow rate 5 mL/h driven by the syringe pump. In addition, the trapping experiments under flow field disturbance were conducted to verify the cell trapping stability of this device. The flow field disturbances were realized by the alteration of fluid velocity. First, HEK293T cell was captured at a fluid velocity of 5 mL/h, then the cell medium fluid flow rate was increased to 30 and 50 mL/h respectively via syringe pump. Eventually, in order to validate the ability of loading dynamic biochemical signals in this new microfluidic device, we injected the fluorescence solution (rhodamine-6 solution) into trapping chamber. More specifically, it was implemented by dynamically altering the flow rates of the fluorescent solution from 9 to 0.09 mL/h. And then the fluorescence intensity near the trapping point was measured and analyzed by describing the changes of the gray value at the same place in different time using MATLAB.

Microfluidic-based single cell trapping using a combination of stagnation point flow and physical barrier

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3 Results 3.1 Height-averaging velocity along the central axis x If the resistance channel 12 (see Fig. 3) is totally blocked, the height-averaging velocities along the central axis x at different flow rates (1 and 5 mL/h, respectively) can be analytically computed by Eq. (9). To validate the analytical solutions, three dimensional (3D) numerical simulations were conducted using computational fluid dynamics (CFD) package ANSYS 15.0 (Ansys Inc). Briefly, the cell trapping chamber was divided into the hexahedral and tetrahedral grids (135564 nodes, 120720 elements) in the Workbench Mesh, full Navier–Stokes equations under steady flow were solved in FLUENT 6.3. The inlet velocities were set to 0.926 and 0.185 m/s corresponding to the flow rates of 5 and 1 mL/h, respectively. All the geometrical and fluid parameters used in all the simulations are listed in Table 1. Figure 5 shows the comparison of analytic solutions and 3D CFD simulation results for the height-averaging velocity along the central axis x in the cell trapping chamber with different flow rates Q. It is clear that along the central axis x, the height averaging velocity nonlinearly increases from zero (at the trapping point) to a certain value (at the inlet) for the different flow rate, and the analytical solutions exhibit good

Table 1 Geometrical and fluid parameters for analytical and 3D numerical simulations Parameters

Values

Length L(x-direction)

1 mm

Height H (z-direction)

30 μm

Width of inlet W (y-direction)

50 μm

Viscosity of fluid

0.001 Pa · s

Fig. 5 The height-averaging velocities along the central axis x by analytical and 3D CFD simulations

Fig. 6 A trapping track of single 293T cell

agreement with the 3D CFD simulation results, demonstrating that our analytical solutions have sufficient accuracy. 3.2 Single cell trapping As shown in Fig. 6, a cell marked with a red arrow from the entrance of the trapping chamber flowed into the chamber almost along the central axis towards the trapping point. In the front and middle part of the chamber, the cell had a faster speed (Fig. 6a and 6b). While the cell moved through the tail of the chamber, its moving speed became slower and got close to zero near the trapping point (Fig. 6c–e). Finally, the cell was stopped at the trapping point (Fig. 6f). The trapping process can be seen in the supplementary material (ESM.mov). 3.3 Stable trapping under flow disturbances After 293T cell was captured, the flow rate of the medium was altered from 5 to 30 mL/h and 50 mL/h, respectively. As shown in Fig. 7a–c, the cell was in the position of the captured point stably. It was also clearly observed from the enlarged part marked in the red box that when the flow rate of the medium was 5 mL/h, the captured cell did not completely contact the channel walls (Fig. 7d). After increasing to 30 mL/h, the captured cell completely contacted the walls (Fig. 7e). When the flow rate was increased to 50 mL/h, the captured cell had a slight deformation, and its small part was pushed into the resistance channel (Fig. 7f). Even if the flow rate was increased by 10-fold, which caused a huge disturbance in the flow field, the captured cell was still stably located at the trapping point. By comparing these three cases shown in Fig. 7, it can be seen that the newly captured cell did not fully contact the sidewalls of the chamber (Fig. 7d), demonstrating the cell

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Fig. 7 Single cell trapping under flow disturbance Fig. 8 Loading of biochemical signals. a Fluorescence images near the trapping point at different time. b Actual signals normalized to a maximum and the fitted result

trapping was not entirely caused by the blocking of side walls, but by the combination of zero flow velocity and physical barrier of side walls. 3.4 Loading of dynamic biochemical signals Eventually, one type of dynamic fluorescein signal implemented by altering the flow rates of the fluorescent solution in every 10 s from 9 to 0.09 mL/h was loaded into the microchannels and the flow chamber from the inlet 2, acting as an approximate square wave input signal whose period was 20 s. And then the fluorescein intensities at the trapping point were recorded. The fluorescence images near the trapping point at different time were given in Fig. 8a. The actual data were normalized to the maximum of the gray value and the fitted result is shown in Fig. 8b. This completely demonstrated that it was easier and more convenient to load biochemical stimuli to the trapped cell in this type of micro-device due to the convection and diffusion [22].

4 Discussion In previous investigations, hydrodynamic-based single cell trapping was primarily based upon either physical barrier or stagnation point flow. The designs based on physical barriers can guarantee the stability of cell trapping with high throughput, but they may cause mechanical damage and are unable to load biochemical signals to the trapped cells precisely, especially to the single cells captured in the latter traps in the serial

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trapping arrays [15–17]. Cellular mechanical damage was negligible in the stagnation-point-flow-based cell trapping as the flow velocity is zero at the trapping point (stagnation point). However, in this way, it greatly increases the cell loss ratio and decreases the trapping stability and the accuracy of loading signals [18] due to the unsteadiness of the flow field and stagnation point. Although these weaknesses can be overcome by adding external feedback controller [19], the introduction of external feedback controller increases the cost and complexity of its implementation. Thus, in this study, a new microfluidic-based hydrodynamic device combining stagnation point flow with physical barrier is proposed for stable trapping of single cells and conveniently loading of biochemical signals. The shape of the trapping flow chamber in this microfluidic device was inspired by the design of a linear shear stress flow chamber based upon the principle of stagnation point flow by Usami and his colleagues [23]. In order to realize an automatic and stable single cell trapping, the resistance channel connecting the chamber and outlet played a critical role. Once the resistance channel was completely blocked by a trapped single cell, the height-averaging velocity along the middle axis of the cell tapping chamber decreased from a maximum (at the inlet) to zero (at the trapping point), which was confirmed by both analytic and 3D numerical simulation studies (Fig. 5). However, if the cell was disturbed and deviated from the trapping point by the change in the flow field, the entrance flow in the resistance channel 12 would ensure that the cell stays at the original position. The feasibility of this novel device was validated by experimental studies. It

Microfluidic-based single cell trapping using a combination of stagnation point flow and physical barrier

can be readily seen from Figs. 6 and 7 that the cell trapping was realized by the proposed device with the combination of zero flow velocity and physical barrier of side walls. Generally, any cell with a size larger than the width of the resistance channel 12 (5 μm) can be trapped using this device. In addition, it was easier and more convenient to load biochemical stimuli to the trapped cell with negligible shear stress as the velocity approximately equals to zero at the trapping point in this type of microdevice (Fig. 8). Although the proposed micro-device for single cell trapping has the aforementioned advantages, there are still some limitations. For example, once one single cell is trapped the remaining cells are just washed away with flow. Such a strategy has low efficiency. However, the current design can be extended to a radial array with many of the same chambers and trapping points to improve the throughput in our future study. Our future study will also include a sophisticated investigation about how the deformability/size of the cell will affect the trapping rate, which would help us to know how to trap a specific cell by this designed micro-device. In summary, a microfluidic-based hydrodynamic device for single cell trapping and dynamic biochemical signal loading is designed based upon a combination of both stagnation point flow and physical barrier to overcome the shortcomings in the previous hydrodynamic-based single cell trapping using either physical barriers (contact-type tweezers) or stagnation point flow (non-contact-type tweezers). It is verified by experimental studies that the micro-device can effectively trap single cells in vitro even under large flow disturbance. And it can also easily load dynamic biochemical signals to the trapped cell. This hydrodynamic micro-device would provide a simple yet effective experimental platform for further study of the relationship between single cells and their dynamic biochemical microenvironments. Acknowledgments The project was supported by the National Natural Science Foundation of China (Grants 11172060 and 31370948).

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