Ultralow and Dynamic Flow Field Generator Composed of Microfluidic Peristaltic Pump

Precise control over flow rate and flow pattern is critical for investigating the contribution of shear force in cellular responses, biofluidic transport, and living matter in a flowing environment. Generation and control over the ultralow flow fields at microscale are, however, difficult, due to thermal agitation and fluctuations in the surrounding environment. Herein, pa novel microfluidic flow field generator is proposed, capable of generating stable flow field down to the limit of thermal noise. Integrated with a customized MATLAB program controlling timely open–close of 18 monolithic PDMS valves, the flow generator outperforms the existing methods by both achievable low flow rate, that is, 0.01 nL s−1, temporal resolution of flow rate fluctuation down to 100 ms, and provides complex flow patterns. Moreover, unlike external devices (e.g., the syringe pump), the design can be easily integrated into any fluidic chip and sealed from the disturbance of experimental conditions, for example, the airflow and the movement of connected pipelines. The methodology is, therefore, suitable for biological and biophysical studies requiring a well‐defined flowing environment.


Introduction
It is well established that physical environmental conditions play important roles in regulating life machinery. [1][2][3][4][5] To date, efforts have been devoted to reconstructing the environmental conditions in vivo for biological and biomedical studies, for example, tissue development, immune responses, and tumor metastasis. [6][7][8][9] Within the biological fluids, shear stress is one of the ubiquitous environmental cues experienced by stem cells when they are being differentiated or expanded in perfusion cultures [10][11][12] and contributes greatly to collective cellular responses. [6,13,14] The main techniques help control the flow field in the microenvironment where single and population cells habitat include syringe pumps, [10,15] peristaltic pumps, [16] and rocker platforms with gravity-driven flow. [10,17,18] Ideally, all the aforementioned devices can generate a low flow rate via adjusting the operational parameters, for example, the rotor speed of syringe and peristaltic pump and the microscale channel size for gravity-driven flow. [10,15,16] While, for an external flow generator, the fluidic volume transmitted with the specific flow velocity in the channel is often subjected to violent fluctuations by incontrollable experimental conditions such as the tubing connection, mechanical vibration of the device, thermal agitation on tubing, and therefore requires recalibration for each experiment. Although gravity-driven flow requires no external controller, the nanoscale channels, which are necessary for maintaining ultralow flow rate, are difficult to fabricate and hardly manipulate in practical circumstances. [19,20] Therefore, a flow field controller, which can be integrated into any fluidic chip and be used to generate complex flow patterns, is highly demanding.
In this study, we present an approach for the generation of ultralow and dynamic flow fields in microscopic structures. Liquid volume as small as 3 nL can be accurately transported by the digitally actuated peristaltic pump, whose cycling time and on-off sequence of involved polydimethylsiloxane (PDMS) membrane valves determine the flow pattern. The fluctuations in flow rate, which are intrinsic to a peristaltic pump, are mediated by connecting the microscopic fluidic channel to a miniaturized water tank, that is, the flow field filter. Our results demonstrate that using the proposed device, fluctuations in flow velocity can be lowered to less than 5% of the original value, and flow rate as low as 0.01 nL s À1 can be generated in microfluidic channels, which are 100 μm in width and 25 μm in height.

DOI: 10.1002/aisy.202200366
Precise control over flow rate and flow pattern is critical for investigating the contribution of shear force in cellular responses, biofluidic transport, and living matter in a flowing environment. Generation and control over the ultralow flow fields at microscale are, however, difficult, due to thermal agitation and fluctuations in the surrounding environment. Herein, pa novel microfluidic flow field generator is proposed, capable of generating stable flow field down to the limit of thermal noise. Integrated with a customized MATLAB program controlling timely open-close of 18 monolithic PDMS valves, the flow generator outperforms the existing methods by both achievable low flow rate, that is, 0.01 nL s À1 , temporal resolution of flow rate fluctuation down to 100 ms, and provides complex flow patterns. Moreover, unlike external devices (e.g., the syringe pump), the design can be easily integrated into any fluidic chip and sealed from the disturbance of experimental conditions, for example, the airflow and the movement of connected pipelines. The methodology is, therefore, suitable for biological and biophysical studies requiring a well-defined flowing environment.

Design and Principle of the Flow Controller
The flow field is generated in the proposed microfluidic device via open/close of PDMS membrane valves, that is, the Quake's valve. [21] In brief, when the thin membrane is deflected by hydraulic actuation, the liquid underneath is forced to move forward, generating pulsed flow fields ( Figure S1, Supporting Information). When the pressure is released, the liquid moves backward. To quantify the reciprocating flow, for example, the flow rate, flow velocity at the center of the channel cross section is measured by tracking the passive particles of 1 μm in diameter (Movie S1, Supporting Information). This velocity obviously depends on the valve responding time (i.e., the timespan for the valve to be fully closed), and the number of valves, which are simultaneously open or closed.
To generate continuous flow, a set of three or more independent microfluidic valves are required, which are composed of a peristaltic pump ( Figure S2, Supporting Information). [6,21] The timely open/close of these valves in a programmed sequence (i.e., 100-110-010-011-001-101) drives a defined volume of liquid from one side to another, where "1" represents the deflected membrane valve (i.e., valve close state) and "0" represents the released membrane valve (i.e., valve open state) ( Figure S2a, Supporting Information). Notably, only transitions from 100 to 110 and 010-011 move liquid forward. The flow rate remains 0 at the other steps ( Figure S2b and S2c, Supporting Information). When the operating frequency is high enough, the new liquid volume is pushed forward before the flow rate goes down to 0, and therefore generates continuous flow, whose flow rate is determined by the valves' sequential operation frequency and the number of valves involved. Fluctuation in flow rate is, however, intrinsic to the peristaltic pump.
To compensate for the decrease in flow rate between steps of programmed valve operation, a minimum of six peristaltic pumps (i.e., the multiplex inlets) are assembled (Figure 1a-c). Via the coordinated action of 18 valves with defined phase mismatching between one another, equal volume of liquid is transferred from one side to another at each step ( Figure 1c). The dropped flow rate during the operation of one peristaltic pump (shown in Figure S2, Supporting Information) can, therefore, be compensated by another pump, whose operation cycle is one step behind. The cycling sequence starts from 111 111 111 111 111 111, where all valves are closed, and ends with 101 010 001 110 011 100 after 11 steps (Section S1, Supporting Information). By monitoring particle velocity at the checkpoint (Figure 1a), our results demonstrate that even though the continuous flow is generated at a step interval of 1 s (i.e., the time difference between programmed valve state), fluctuation in particle velocity remains obvious (Figure 1d,e, Supporting Information). Fast Fourier transform (FFT) analysis shows a dominant frequency of %1 Hz, indicating that the fluctuation is caused by the sinusoidal flow rate variation intrinsic to Quake's valve open/close operation ( Figure S1, Supporting Information).
To achieve an even lower flow rate, we integrate a flow distributor into the chip (Figure 1a and 2a). The flow field in the tree bifurcation structure [22,23] was first estimated using COMSOL Multiphysics software based on the finite-element method (Figure 2b,c).
Since each subchannel of the flow distributor carries the same geometry, the flow rate at all positions can be calculated by where v in is the input velocity and i is the level of the diversion channel. The flow rate can, therefore, be decreased to 2 Ài times the input value (i.e., dividing 1/4, 1/32, and 1/128 times) (Figure 2a-c), which is consistent with our experimental observations using particle tracking (Figure 2d), respectively. Even though fluctuation is hardly visible in 1/32 and 1/128 subchannels (Figure 2d), variations in flow rate can still be reflected by particle velocity, that is, 390 AE 10 and 90 AE 3 μm s À1 .
To further eliminate the fluctuation in flow rate, we integrate a flow field filter into the microfluidic chip (Figure 1a and 3). According to Joukowsky equation, [24] sudden changes in flow rate Δv lead to varying pressure ΔP, and their correlation can be written as where ρ is the fluid mass density and c is the speed of sound in the fluid. [24,25] When a miniature water tank is connected to the fluidic channel, variations in pressure can then be reflected as changes in the height of the liquid-air interface, Δh (Figure 3a-c), that is where g is the gravitational acceleration. Liquid volume change in the tank, Q 1 = πR 2 Δh (where R is the radius of the water tank), can then mediate the fluctuations in the input flow rate. For example, when the filter is turned on, a change in flow velocity at point 1 from v to v 0 leads to varying pressure at the channel division part ΔP and thus changes the height of liquid-air interface Δh, that is, ðv 0 À vÞ ¼ g c ðΔhÞ according to Equation (2) and (3). The liquid volume change in the tank can be calculated as Q 1 ¼ πR 2 ðΔhÞ ¼ πR 2 c ðv 0 ÀvÞ g . The total volume Q passing through the cross section of point 2 is then where Q 2 is the input liquid volume (Point 1) and duration Δt.
Obviously, decreased input flow rate (v 0 < v) lowers the liquid volume in the tank, which is directed to go through point 2 by laminar flow [26] and contributes to the increased output flow rate. On the other hand, the increased flow rate (v 0 > v) leads to increased pressure and thus increased liquid volume in the tank, causing decreased output flow rate. The fluctuation in the input flow rate can, therefore, be mediated by the flow field filter. The capacity of the filter depends on the coordination between fluidic channel geometry (i.e., x, y, and R) and the control parameters of input flow (i.e., v and Δt) (Section S2, Supporting Information). Our results demonstrate that using the flow field filter, the velocity of input flow at 25.8 AE 7.3 μm s À1 is effectively tuned to 18.1 AE 0.2 μm s À1 in 1/2 subchannel (Figure 3b), where the fluctuation in flow velocity is reduced by %50 times. In contrast, when the flow field filter is turned off, the flow velocity at the same position returns to 19.3 AE 8.1 μm s À1 . We, therefore, conclude that using the aforementioned functional modules (i.e., a hierarchical peristaltic pump, flow distributor, and flow field filter), the flow velocity in the microfluidic channels can be regulated down to the level of Brownian motion of the tracking particle at noise level (i.e., mean velocity of 0.5 μm s À1 ). [15,27]

Effect of Controllable Flow Shear on 3T3 Fibroblast Response to TNF-α Stimulation
We, then, use the proposed microfluidic chip to investigate the effect of flow shear and the implemented dynamic noise on the response of mammalian cells. First, we cultured 3T3 fibroblasts in the subchannels. Tumor necrosis factor (TNF-α) at 0.1 ng mL À1 concentration is delivered to population cells at defined flow rates and flow patterns. The immune responses of population 3T3 fibroblasts are reflected by fluorescence distribution of NF-κB-p65-dsRed molecules, that is, in cytoplasm and nuclear (Figure 4a,b, and Movie S2, Supporting Information). For example, the dynamic nuclear localization of NF-κB-p65-dsRed can be assessed by quantifying the summed dsRed fluorescence intensity in individual cells' nucleus. [28] We observed that when there is no shear flow, that is, TNF-α is delivered to 3T3 fibroblasts by diffusion using a previously published microfluidic device, the fraction of responsive cells is %18%. [6] However, at low flow rate (i.e., 0.01 nL s À1 ), minor  www.advancedsciencenews.com www.advintellsyst.com increase in number of responsive cells was observed with filtered TNF-α input, that is, when the flow field filter is turned on (Figure 4c). Maintaining the "filter-on" state, increasing flow rate up to 1 nL s À1 leads to lowered fraction of responsive cells by nearly 10% (denoted by black circles in Figure 4c). One of the possibilities is that the physical interactions between TNF-α and receptors on the cell membrane are associated with their local concentration, which is sensitive to the differences in mass transportation mode of TNF-α molecules, for example, diffusion driven by concentration gradient (no flow) and eddy diffusion affected by geometry of the culture environment. [29][30][31] However, the responsiveness of population 3T3 fibroblasts is evaluated by counting the total number of responsive cells within 1 h of TNF-α stimulation, which far exceeds the timespan required to reach equilibrium concentration distribution. Moreover, our results demonstrate that the effects of shear flow disappear when the flow field filter is turned off (red circles in Figure 4c). These results indicate that factors other than ligandreceptor interactions affect individual cell's immune responses.
Our previous studies reveal that dynamically varying mechanical forces cause cytoskeleton remodeling and chromatin conformational changes, which affect transcription activities, [14] and pico-Newton forces cause chromatin conformational and structural changes. [32][33][34] It is, therefore, plausible that when TNF-α molecules are delivered to fibroblasts with unchanged flow velocity, cytoskeleton network and chromosome of individual cells are positioned under constant shear, which causes tensed nuclear conformation and affects TNF-α-stimulated signaling. [35] The application of noisy physical cues (i.e., input flow with "filter-off"), on the other hand, brings no obvious changes to the responsiveness of population cells. We suspect that cell deforms under shear force. Fluctuations in flow rate leads to oscillating nuclear and cytoskeleton conformation. Assuming cell is forced to an "inactive" state under shear, which is reflected by dropped responsive rate, the variations in flow velocity allow the cell to temporarily regain its relaxed form, that is, "active" state. As an elastic body, the fluctuation amplitude in cellular volume and intracellular structures (i.e., cytoskeleton and chromosome) depends on both force amplitude and varying frequency, which is a physical property intrinsic to individual cells. [36] Consistently, at defined flow rate fluctuation frequencies ranging from 1 to %0.01 s À1 , the responsiveness of population fibroblasts returns to the value of control samples (no shear) (Figure 4d). Changing the fluctuation frequency in flow rate by regulating the interval between valve operation steps till 0.1 s (corresponding to frequency of 10 s À1 ) fails to release cells from the "close" state ( Figure 4d). These experiments demonstrate the feasibility of our approach in precisely controlling the flow velocity in microscale spaces and reveal that the noises intrinsic to the flowing environment in vivo help population cells resist the negative effects of shear forces.

Conclusion
In this work, we presented a microfluidic chip integrated with a flow field controller, a flow distributor, and a multigear peristaltic pump. By timely control of 18 PDMS membrane valves, dynamic variations in flow rate with controllable noise input can be achieved, which outperforms most existing flow Figure 4. Cellular response to frequency precisely controlled TNF-α stimulation. a) In the unstimulated state, NF-κB-p65 molecules remain in cells' cytoplasm, reflected by fluorescence distribution. b) Nuclear localization of NF-κB-p65 molecules after TNF-α stimulation. c) The response rate (i.e., the fraction of responsive cells) to TNF-α stimulation with and without the flow field filter, that is, the fluctuation in flow rate. d) The correlation between population cells' responsiveness and the frequency of variation in flow rate during TNF-α stimulation. Scale bar denotes 10 μm.
www.advancedsciencenews.com www.advintellsyst.com generators. [10,17,18,37] Moreover, the presented microfluidic setup requires no external connection and thus resistance to the disturbance of different lab setups. With the proposed microfluidic setup, the questions, for example, the effect of dynamically varying physical signals on immune responses, can now be addressed.

Experimental Section
Chip Fabrication: First, we prepared the control and flow layer of the multilayer PDMS chip via photolithography and soft-lithography techniques as described elsewhere. [38] Different layers of the chip were bonded on top of one another via prior exposure to O 2 plasma. Subsequently, holes were punched into the resulting PDMS device, where inputs and outputs were connected, and were then bonded to glass after a second plasma treatment.
Cell Culture and Chemical Stimulation: NIH-3T3 p65 À/À fibroblast cells were transfected with p65-dsRed for quantification of NF-κB nuclear localization in response to TNF-α stimulation. [6,14,39] For the adherent culture of 3T3 fibroblasts, the chip was treated with fibronectin (Chemicon International Inc., 25 μg mL À1 in PBS) for at least 40 min and washed with a culture medium before cell loading.
Cells were harvested at 80% confluence with trypsin, resuspended, and loaded into chips through a semiautomated loading program at a cell density of 10 6 mL À1 . The cells were then kept in the chip for 4 h before TNF-α stimulation. The environmental conditions (i.e., 37°C and >98% humidity and 5% CO 2 ) were maintained using a customized live cell imaging system (RongLight, China).
Flow Field Generation Using Fluidic Chip: In brief, to generate flow field in the microfluidic channels, liquid was first loaded into the inlets by pressurizing the connected centrifuge tubes and driven into microfluidic channels by programmed operation of six peristaltic pumps, each of which is composed by three monolithic valves (Figure 1a). Liquid volume from six connected microchannels mixed into one. The flow rate in the main channel was, therefore, determined by cooperative operation of six peristaltic pumps. When flow passed by the flow field filter, the variations in flow rate caused upward or downward movement of liquid-air interface in the water tank, leading to back-and-forth movement of liquid in the connected microchannel. The filtered flow was then directed to the flow distributor with a tree bifurcation structure, where the flow rate was further lowered.
Flow Field Tracking and Analysis: Polystyrene beads (diameter 1 μm, emitting red fluorescence light) were suspended in DI water and diluted to 100 particles per 0.045 mm 2 before being introduced into the PDMS chip. Performance of the multigear peristaltic pump, flow distributor, and flow field filter could then be reflected by recording the movement of particles in the central region of the microfluidic channels, that is, 40Â objective at a frame rate of 10 fps. Positions of individual particles were identified and linked to smooth trajectories using TrackMate routine of ImageJ software.
The Finite Element Method: To simulate flow field in the tree bifurcation structure of flow distributor, COMSOL Multiphysics software was used. The basic function was the Navier-Stokes equations of incompressible fluid.

> <
> : where ρ, t, u, p, and μ are the density, time, velocity vector, pressure, and dynamic viscosity of the solution, respectively. The simulated fluid was pure water at 25°C with ρ of 0.997 Â 10 3 kg m À3 and μ of 0.897 Â 10 À3 Pa s À1 . The boundary conditions for the fluid flow are listed as follows: 1) channel wall was set to be no-slip boundary condition; 2) sinusoid variation in flow rate was set as the input; and 3) the pressure was set to be 0 at all the outlets. Image Acquisition and Data Analysis: For image acquisition, Nikon Ti2-E inverted microscope with an automated translational stage and a digital complementary metal-oxide semiconductor (CMOS) camera (ORCAFlash4.0, Hamamatsu, Japan) and a customized live-cell culture system (RongLight, China) were used. The stage and image acquisition were controlled via the NIS Elements software (Nikon, Japan), and the live-cell culture system was a one-touch start with automatic control of the culture conditions including 37°C, >98% humidity and 5% CO 2 . Both bright-field and fluorescent images were acquired and analyzed via a customized MATLAB (MathWorks, USA) program. The algorithm extracted the position of nuclear centroids, and the fluorescent intensity of nuclear and cytoplasmic, using which the cell motivation and fluorescent intensity, were quantified.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.