Multiple independent autonomous hydraulic oscillators driven by a common gravity head

Abstract

Self-switching microfluidic circuits that are able to perform biochemical experiments in a parallel and autonomous manner, similar to instruction-embedded electronics, are rarely implemented. Here, we present design principles and demonstrations for gravity-driven, integrated, microfluidic pulsatile flow circuits. With a common gravity head as the only driving force, these fluidic oscillator arrays realize a wide range of periods (0.4 s-2 h) and flow rates (0.10-63 μl min^-1 ) with completely independent timing between the multiple oscillator sub-circuits connected in parallel. As a model application, we perform systematic, parallel analysis of endothelial cell elongation response to different fluidic shearing patterns generated by the autonomous microfluidic pulsed flow generation system.

ARTICLE

Received 31 Aug 2014 | Accepted 24 Apr 2015 | Published 15 Jun 2015

Self-switching microuidic circuits that are able to perform biochemical experiments in a parallel and autonomous manner, similar to instruction-embedded electronics, are rarely implemented. Here, we present design principles and demonstrations for gravity-driven, integrated, microuidic pulsatile ow circuits. With a common gravity head as the only driving force, these uidic oscillator arrays realize a wide range of periods (0.4 s2 h) and ow rates (0.1063 ml min 1) with completely independent timing between the multiple oscillator sub-circuits connected in parallel. As a model application, we perform systematic, parallel analysis of endothelial cell elongation response to different uidic shearing patterns generated by the autonomous microuidic pulsed ow generation system.

DOI: 10.1038/ncomms8301

Multiple independent autonomous hydraulic oscillators driven by a common gravity head

Sung-Jin Kim1,2, Ryuji Yokokawa2,3, Sasha Cai Lesher-Perez2 & Shuichi Takayama2,4,5,6

1 Department of Mechanical Engineering, Konkuk University, Seoul 143-701, Republic of Korea. 2 Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA. 3 Department of Micro Engineering, Kyoto University, Kyoto 615-8540, Japan. 4 Department of Macromolecular Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA. 5 Biointerfaces Institute, 2800 Plymouth Road, NCRC Building 10 A183, Ann Arbor, Michigan 48109, USA. 6 University of Michigan Center for Integrative Research in Critical Care (MCIRCC), Building 10-103A, North Campus Research Complex, 2800 Plymouth Road, Ann Arbor, Michigan 48109, USA. Correspondence and requests for materials should be addressed to S.T. (email: mailto:[email protected]

Web End [email protected] ).

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Although the electronicuidic analogy1,2 is commonly inferred, microuidic circuits that can simultaneously perform multiple independent parallel operations in an

autonomous fashion have yet to be implemented. Constant-voltage electronic circuit designs allow instructions to be embedded in the arrangement of circuit components in a way that multiple tasks can be performed autonomously and independently in parallel (Fig. 1a). This enables electronic circuits to be automated and user-friendly while also being versatile and multifunctional. Microuidic circuits, however, still require instruction from external controllers and do not

demonstrate independent parallel processing capabilities. Even microuidic logic circuits37 generally require instruction from computer-programmed, time-varying input pressures and thus do not operate autonomously. Our previously described constant ow-driven oscillator circuits can generate pulsatile ows autonomously but cannot generate independent, parallel ows811. A uidic astable multivibrator driven by a constant pressure source was described 20 years ago, but without multiplexing or application demonstrations12.

Here, we describe microhydraulic circuits that implement autonomous and independent parallel ow-switching in a manner similar to capabilities of constant-voltage electronic circuits. Using a gravity water head (0.30.7 m) as the driving force, the circuits perform embedded instructions in multiple parallel sub-circuits (Fig. 1b). Our practical goal is to replace off-chip controllers13,14 that generate time-varying input pressure with gravity-driven, autonomous ow-switching schemes to facilitate parallel, long-term cellular studies of biorhythms1520, emulating rhythmic stimulation such as those imposed by vascular ow and periodic hormone release. Similar to how low-voltage circuit design concepts were initially niche applications in the watch industry and later became indispensable in sophisticated electronics21,22, we believe that scalable low-pressure hydraulic circuit design concepts will have implications beyond our initial cell applications to become critical modules for a broad range of sophisticated microuidic operations. As a model application that takes advantage of these capabilities, we systematically analyse endothelial cell elongation in response to different shear stresses and ow-switching periods.

ResultsOperation principles of oscillator sub-circuits. Figure 2a shows an actual image of an oscillator array and a close-up schematic of one oscillator sub-circuit. As shown in the inset of Fig. 2a, the

Voltage

Pressure

Time

Time

Battery

Input well

Electronic circuit Constant pressure-driven oscillator array

Independent timing between sub-circuits

Current

Flow rate

Time Time Time Time

Independent timing between sub-circuits

Figure 1 | Electronicuidic analogy of instruction-embedded oscillator arrays. (a) Electronic circuits with embedded instructions to perform multiple parallel operations with independent timing are typically driven by a constant-voltage source. (b) Hydraulic oscillator system described in this paper. This circuit has embedded instructions to produce multiple parallel periodic ows with different ow rates and independent timing using a constant gravitational potential as the driving uid input source.

Input wells

Waste wells

i1

Microfluidic oscillator

i2

Hi

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SC 2

SC N

Osc. period control +

4 mm

o11 o12 o21

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o22 oN1 oN2

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Figure 2 | Gravity-driven microuidic oscillator. (a) An image of an oscillator array chip and schematic of one oscillator sub-circuit. Height difference between input wells and the oscillator chip applies a constant pressure on the oscillator sub-circuits. The inset shows the schematic of an oscillator sub-circuit, which consists of microuidic component such as microuidic resistors and capacitors. The microuidic resistors are channels and the capacitors are chambers having elastomeric membranes. As shown in the cross-sections of the schematic, the valves and capacitors have a top layer (grey), a bottom chamber layer (dark yellow) and an elastomeric membrane (pink). The deections of the membranes shown are what state the membranes would be in right after the opening of valve 2. Scale bar, 4 mm. (b) Circuit diagram of the oscillator. Each sub-circuit (SC) is connected in parallel. Sub-circuit i (i 1 to N) has

two outlet ports (oi1 and oi2). The inset presents the circuit diagram of the oscillator sub-circuit, which corresponds to the inset of a. Cj (j 1, 2) is mechanical

capacitance by an elastomeric membrane. Rrj and Rfj represent the uidic resistances of reference resistors and ow resistors, respectively.

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sub-circuit is composed of a three-layer structure including a thin-membrane middle layer, and top (grey colour) and bottom (dark-yellow colours) layers. These sub-circuits are comprised of microuidic resistors (channels), capacitors, valves and a reference well. Microuidic capacitors are chambers with elastomeric membranes that store pressure-related energy by membrane deformation. Valves are similar to the capacitors, except with much smaller membrane areas and a protrusion in the top chamber that leads to ow shut off. The reference well is a reservoir lled with liquid that is open to the atmosphere. The key design points are: to have the bottom chamber of the capacitor downstream of one valve connected to the bottom actuation chamber of the other valve, and to have reference resistors that connect the pair of interconnected capacitorvalve bottom chambers via a reference well (the insets of Fig. 2a,b). Importantly, the uid owing through and out of the top chambers of the device remains separate from the bottom chamber uid that connects the two valves to each other for actuation. In addition, owing to the reference well being open to atmosphere, the bottom actuation chamber pressures can increase and decrease somewhat independently from the upper ow-through chambers. Having an output pressure (Po) lower than the reference well pressure is also indispensable for being able to have valve closings23.

How do the microhydraulic oscillator sub-circuits, described in this paper, trigger alternating valves to open and close with a constant input pressure (Pi)? Consider the top-side pressures of capacitors 1 and 2, PC1t and PC2t, respectively (Fig. 3a). When valve 1 opens, PC1t increases from BPo to Pi ( 9 to 3 kPa, see

Fig. 3b), where for a given pressure head, the value of PC1t will

depend on the relative values of capacitor 1s upstream and downstream uidic resistances (Supplementary Fig. 1). Importantly, an increase in PC1t concomitantly increases the bottom pressure of capacitor 1 (PC1b), which is connected to valve 2, resulting in the closure of valve 2. While PC1b is high (9 kPa)

immediately after valve 1 opens, the pressure gradually decreases over time as the pressurized uid ows through the reference well and resistors towards capacitor 2 (inset ii of Fig. 3c). As a result, while PC1b decreases PC2b increases. Once PC1b is low enough (1 kPa), valve 2 opens thereby abruptly raising PC2b and closing

valve 1 (inset iii of Fig. 3c). This process is repeated in an alternating manner resulting in oscillations. More detailed pressure relations, and valve-opening and -closing conditions are presented in Supplementary Fig. 2. Note that unlike pneumatic valves, hydraulic valves require a relatively higher bottom pressure than top pressure of the valves to push the membrane into the closed position7,23. We achieve this condition by using a negative outlet pressure Po that reduces PC1t and PC2t and effectively helps valve closing by pulling the membrane into the closed position (Supplementary Fig. 3).

Independent control of oscillation periods and ow rates. To control oscillation periods, we regulate the rate of change of PC1b

and PC2b. As shown in Fig. 3c once valve 1 opens, the open state of valve 1 is maintained until PC1b decreases sufciently. Thus, if PC1b drops slowly (or rapidly), valve 1 remains open longer (or shorter). Note that Pref is constant (0 kPa) and PC1t is also consistently at Pi in the open state of valve 1. Between the two pressure points (Pref and PC1t), capacitor 1 and reference resistor 1 are serially connected. This makes the time constant for the open state of valve 1 to be Rr1C1 (Supplementary Fig. 4); similarly, the time constant for the open state of valve 2 is Rr2C2. Here, Rr1 and Rr2 are the uidic resistances of reference resistors, and C1 and C2 are the mechanical capacitances of capacitor 1 and 2, respectively (see Fig. 2a,b). We modify Rr1 and Rr2 across the sub-circuits to generate differential oscillation periods. On the other

hand, output ow rate is determined by the uidic resistance of ow resistors (Rf1 and Rf2, see Fig. 2b). When valve 1 is open, PC1t is Pi and outlet pressure is Po. Thus, the ow rate through ow resistor 1 is (PiPo)/Rf1. Similarly, when valve 2 is open, the ow rate through ow resistor 2 is (PiPo)/Rf2. Simply put, the micro-oscillator schematic can be broken into two functional compartments: one to determine the oscillation period and the other output ow rate, respectively, the light red-shaded and light green-shaded regions in Fig. 2b.

Beyond being able to use a convenient gravity head as the pumping force, a fundamental utility of the oscillator array is that its sub-circuits can be connected in parallel, from the same gravity-driven pressure source, yet have completely independent oscillation frequencies without noise or crosstalk. To show the operational range and the parallel processing ability of our oscillator array, we constructed two distinct oscillator arrays: oscillator array A has fast oscillation periods and high ow rates, whereas oscillator array B has slow oscillation periods and low ow rates; see Supplementary Movies 1 and 2. Detailed parameters of the two oscillator components are presented in Supplementary Fig. 5. In sub-circuit Ai (i 1, 2, 3) of oscillator

State 1

State 2

Pi

A

A

A

B

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B

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Figure 3 | Self-switching mechanism of the two valves of an oscillator sub-circuit. (a) Alternating opening and closing of the two valves. Valve 1 opens in state 1, and valve 2 opens in state 2. Note that when one valve opens, the other valve closes. Dotted blue arrows depict uidic motion passing through the top side of the valves, and this motion becomes the output of the oscillator sub-circuit. Dotted red arrows illustrate the ows through reference channels, and this ow controls the switching period of the valves. Note that the two solution-ows represented by the blue and the red arrows do not mix owing to the membrane middle layer. PCit and PCib (i 1, 2) are the pressures of capacitor is top and bottom, respectively.

(b) Theoretical pressure prole of PC1t. Pi and Po are inlet and outlet

pressures of the oscillator, respectively. (c) Theoretical pressure proles of PC1b and PC2b. Insets i, ii and iii illustrate the open (o) and close (x) states of the valves and uid ows in the bottom layer (red arrows).

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array A, ow resistor 1 (Fig. 2a) is connected to three downstream ow resistors (ai1, ai2, ai3) that have three different uidic resistances, respectively (Fig. 4a). As a result, sub-circuit Ai generates three different uidic pulse amplitudes through ai1, ai2 and ai3 (Fig. 4b). The ow rates of ai1, ai2 and ai3 are 5, 19 and 63 ml min 1, respectively; sub-circuits A1 to A3 open their valves with periods of 0.4, 1.0 and 2.0 s, respectively. Sub-circuit A0 is simply a resistor, so it produces a constant output ow. Figure 4c summarizes oscillation periods of the oscillators, and the inset of Fig. 4c presents the ow rates in ai1 to ai3. Oscillator array B has four sub-circuits, which generate ow-oscillation periods of 10, 20, 66 and 119 min, respectively; two downstream ow resistors connected to each sub-circuit produces ow rates of 0.10 and0.18 ml min 1, respectively (Supplementary Fig. 6).

Cell morphology change under parallel shear stresses. To demonstrate the utility of the oscillator arrays, we simultaneously evaluated the response of endothelial cells to multiple different levels of shear stress and periodic pulse in a single chip. The cells were seeded in resistors ai1 to ai3 of oscillator sub-circuits Ai (Fig. 4a). The sub-circuits A1 to A3 generated periodic ow pulses of 0.5, 1 and 2.5 Hz, respectively, and sub-circuit A0 has a constant ow (0 Hz). The ows in resistors ai1, ai2 and ai3 applied shear stresses of 5, 18 and 58 dyn cm 2, respectively, to the cells.

Figure 5a compares time-lapse images of changes in the cell morphology at 5 versus 58 dyn cm 2 and 1 Hz pulsing for 12 h. The images show that the cells exposed to 58 dyn cm 2 are more elongated than those at 5 dyn cm 2. To quantify the elongation, we use circularity that is dened as 4pA/Lp2. A is the

area of the cell and Lp is the perimeter of the cell. Shear stress has been demonstrated to elongate cells over time, consequently decreasing cell circularity, where circularity is 1 for a circle and 0 for a line. Figure 5b presents the change in cell elongation after 12 h at various levels of shear stress and pulsatile frequencies. The initial mean circularity of the cells in the channels varied from0.57 to 0.63 (relative s.d. 6.4%). To systematically quantify the

inuence of various shear stress levels and pulse frequency on cell morphology, we use relative circularity, which is the circularity at 12 h divided by the initial mean circularity at 0 h. Lower relative

circularity indicates cells are more elongated after 12 h. The results are summarized in Fig. 5c.

We found that as shear stress increased, frequency effects on circularity became more prominent. At each shear stress level, we used an independent two-sample t-test to compare two frequency conditions and identify statistically different cellular elongation. The four frequency conditions assessed produced six combinations of two frequency comparisons at each shear stress condition (the inset of Fig. 5c). At 5 dyn cm 2 shearing, only two out of six combinations were signicantly different. As the shear stress level increased from 18 to 58 dyn cm 2, the combinations of signicantly different pairs increased from 4 to 5 (see

Supplementary Fig. 7 for more details). This result suggests that frequency effects on circularity increases with increasing shear rate. In addition, the trend at 18 dyn cm 2 is different from that at 5 and 58 dyn cm 2. It is important to note that initial cell density varied by 23% in the ow resistors where cells were seeded: the highest and the lowest densities happened at the ow resistors where ow oscillation was 0.5 and 2.5 Hz of 18 dyn cm 2, respectively. This density variation could also be of some inuence on the observed relative circularity changes24.

The angle of orientation, however, did not change signicantly from 0 to 12 h (Supplementary Fig. 8). This result agrees with previous studies25,26, in that cell alignment occurs more slowly than cell elongation. In addition, the cell density remained steady between 470 and 590 cells per mm2 in all channels for the duration of the experiment, assuring that cell attachment was sufcient to resist the shear stress levels generated and that cell detachment was minimal.

DiscussionAnalogy between electronic and hydraulic circuits provides a means to adapt the design of well-established electronic circuits to that of microuidic circuits1,2. Interestingly, microhydraulic circuits that perform autonomous parallel operations driven by a constant water head alone, which also mimic parallel instruction-embedded electronic circuits, are conspicuously missing even when we also consider micropneumatic circuits in addition to microhydraulic circuits. This may in part be due to the prevalent use of macro-solenoid valves for time-varying pneumatic pressure

Pi

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a02 a01 a03 a12 a11 a13 a22 a21 a23 a32 a31 a33

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A1

Figure 4 | Microuidic oscillator array. (a) Photograph and circuit diagram of the multiple sub-circuits (SCs). Scale bar, 2 mm. (b) Theoretical ow proles. Panels from left to right relate to ows in oscillator sub-circuit Ai (i 03). Flow proles plotted in red (top), dark yellow (middle) and blue

(bottom) are ows at resistors ai1, ai2 and ai3, respectively, connected to oscillator sub-circuit Ai. (c) Performance of oscillators A. Filled and unlled points are the experimental and theoretical results, respectively. The error bars are s.d. and were obtained from repeated measurements (n420). The inset show the maximum ow rate (Qmax) and shear stress (t) of resistors ai1, ai2 and ai3 in a.

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5 dyn cm2, 1 Hz

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(dyn cm ) 5

N

6 4 2 0

18 58

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Figure 5 | Simultaneous on-chip testing of cell elongation response to shearing conditions. (a) Time-lapse micrographs showing endothelial cell elongation. Cells at 5 dyn cm 2 show less elongation than those at58 dyn cm 2. Pulse frequency is the same at 1 Hz. Scale bar, 200 mm.

(b) Circularity of cells change signicantly after a 12-h exposure to ows with shear stresses of 5 and 58 dyn cm 2 at all pulse frequencies tested (Po0.001 by paired two-sample t-test at the 5% signicance level).(c) Relative circularity at 12 h. The relative circularity is dened as the circularity at 12 h divided by the initial mean circularity at 0 h. The result is obtained from oscillator array A of Fig. 3a. Error bars of b and c show the s.e. (n 80). The inset shows the number (Nc) of frequency pairing

combinationsout of the six possible combinationswith statistically signicant differences (Po0.05) in relative circularity between them.

inputs4,5,13. More fundamentally, gravity-driven, parallel switching operations cannot be accomplished in microhydraulic circuits simply by mimicking electronic circuit architectures, but must deal with and even take advantage of detailed features unique to hydraulic circuits and their components.

Unlike electrical resistance that scales as radius (r) to the 1/r2, uidic resistance scales as 1/r4. Consequently, uidic resistance increases much more with decreasing device size when compared with electrical resistance. In addition, although electrical and uidic resistances are linearly proportional to electrical resistivity (r) and uidic viscosity (m), respectively, r can be regulated in a wide range by selection of the electron-conducting material, whereas m is xed at a relatively high value for a given solution, regardless of what type of material is chosen for the channel. Specically, r of copper and glass are 2 10 8 and 1 109 Ohm m, respectively, but m of

water is 1 10 3 Pa s. Thus, microuidic circuits with digital

circuit designs37, which inherently require massive serial integration of small components for logic operation, have issues

with large pressure drops. Even with high-pressure actuation and pressure-gain methods5, such digital approaches can limit massively parallel ow control. The device described in this paper uses analogue circuit design concepts to minimize internal resistance for low-pressure operation: by reducing the number of components and lengths of resistive channels a uid must ow through (blue arrow in Fig. 3a); by separating the actuation uid (red arrow in Fig. 3a) from the ow-through uid; and by parallel connection of the sub-circuits. Input pressures of microuidic hydraulic digital circuits5,13 are B100 kPa, which is equivalent to B10 m water head. In contrast, our device only needs a water head of 0.30.7 m (37 kPa). This low-pressure actuation by water head allows device actuation in a typical lab bench or incubator setting.

The ability to use constant pressure inputs and convert them to parallel outputs is just as important as the ability to use low pressures. Unlike the constant-pressure oscillator described here, the input pressure of our previous constant-volumetric ow rate-driven oscillators uctuates; see Fig. 2c of ref. 8. Because the input pressures of the ow-driven oscillators connected in parallel uctuates synchronously, parallel output ows with different ow-switching periods suffer severe crosstalk or are not possible. In contrast, the oscillator array in this report consists of parallel oscillator sub-circuits that switch with completely independent timing from each other. Theoretically, this enables unlimited number of the sub-circuits to work in parallel. The sub-circuits operate with a constant pressure that is provided through the height difference between the reservoirs and the devices. Importantly, we use a negative output pressure to satisfy the negative threshold pressure23 required for our hydraulic valve closing. This is a feature of current hydraulic valves that differ from the switching-off characteristic of electronic transistors.

One may wonder how these microhydraulic circuits compare with their pneumatic counterparts. Although a constant vacuum-driven ring oscillator can generate clock signals for microuidic pneumatic digital logic circuits27, the pneumatic approaches still require other temporally programmed pressure-input pulses to control parallel outputs4, thereby the use of constant pressure input alone for such circuits has not been demonstrated. Digital circuit design concepts also require signicantly larger number of components compared with analogue circuit designs of similar functions (see Supplementary Fig. 9), leading to practical fabrication challenges as well as pressure drop challenges. Finally, unlike microhydraulic circuits where the assay solutions are directly manipulated within the circuit, pneumatic logic circuits require that liquid solutions be manipulated indirectly through a completely separate network of channels.

As an application, we studied cell morphology change within hydraulic oscillator arrays that generate various ow rates and oscillation periods in parallel channels. These devices facilitated a systematic study of the combinatorial effects of shear stress levels and ow-oscillation frequencies on endothelial cell elongation. Previously, a microuidic approach using Braille pins26 was applied to endothelial shearing; however, this work did not independently control ow rate and pulse frequency, because the pin actuation frequency simultaneously affect both parameters, thereby limiting the systematic study of ow rate and pulse frequency on cell morphology. Other devices2831 also have not tested different ow rates and pulse frequencies in parallel channels, at least partially because of the substantial automation required for parallel pulsed shear experiments. Thus, previous devices have been limited in simultaneous screening across a broad range of shear stresses26,28 and pulse frequencies2931.

While the achieved gravity-driven ow rates of0.163 ml min 1 are somewhat limited, it is important to note that this range covers most of the range of ows important for

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biomedical microuidics. At the lower end, 0.02 dyn cm 2 is ideal for culture of delicate cells such as neurons or assays that require gentle ow. The higher ow rates provide shear stresses estimated to be up to 58 dyn cm 2 in our channels enabling exposure of endothelial cells to the higher range of shear stress experienced by cells physiologically. Also, wide oscillation periods(0.4 s2 h) implemented in our oscillator could be used to study various biological rhythms such as periodic shearing by heart beating, periodic hormone secretion and calcium oscillation15,20. Importantly, such applications would be available in an incubator setting owing to the constant low-pressure actuation by a water head. While our work focused on cellular applications, the design principles for constant-pressure-driven, parallel instruction-embedded devices should be applicable for a broad range of applications where microhydraulic devices with multiple independent and autonomous sub-circuits are required.

Methods

Device fabrication. We fabricated the oscillators using soft lithography32. In master molds, the features of reference resistors were fabricated rst by a deep reactive ion etching of a Si wafer and then the other features by SU-8 photolithography. We silanized the master mold with tridecauoro-1,1,2,2-tetrahydrooctyl-1-trichlorosilane (United Chemical Technologies) in a desiccator, and continued it for 4 h to promote facile demolding of casting material. The casting material was made from poly(dimethylsiloxane) prepolymer and curing agent (Sylgard 184, Dow Corning) at a 10:1 ratio. The oscillators for device operation consisted of three layers: the top and the bottom layers having the features of microuidic components were cast against the master molds with a curing temperature of 60 C overnight. The middle layer is a membrane layer (40 and 30 mm-thicknesses for oscillators A and B, respectively), and was spin-coated on a silanized glass slide, and then cured at 120 C for 20 min. Detailed bonding process is shown in supporting information of ref. 10.

Computational simulation and ow-oscillation experiment. For developing the theoretical model of the oscillator, we used a commercial software (PLECS, Plexim GmbH). Detailed circuit diagram of the model and parameters of each microuidic component are presented in Supplementary Fig. 5. For the ow visualization, we mixed a blue food dye. To facilitate the introduction of working solutions, the device was put in a vacuum for 5 min and then in ambient pressure for 40 min. We measured the pressures of device inlet and connection tube outlet from height difference between the reservoirs and the oscillator, and the connection tube outlet and the oscillator, respectively. Working solutions were deionized water. Maximum ow rate (Qmax) was calculated by Poiseuilles law, Qmax Dp/R. Here, Dp is the

pressure difference between device inlet and connection tube outlet, and R is a uidic resistance between the inlet and outlet pressures. Shear stress (t) was calculated by t 6mQmax/(wh2), where m is the dynamic viscosity and w and h are the

width and height of a ow resistor, respectively.

Cell culture and imaging. For the shear ow experiment, we used human umbilical vein endothelial cell (HUVECs). HUVECs were cultured in endothelial cell growth media (CC-3162, Lonza) under 37 C, 5% CO2 on T-25 asks. Then,0.25% Trypsin/EDTA (Gibco) was used to detach cells from the asks. For the cell seeding in the ow resistors, laminin (10 mg ml 1 in PBS) was injected along the ow resistors and incubated in a CO2 incubator for 1 h to coat the resistor surface. Then, the laminin solution was carefully washed with PBS, and cells were injected into the resistors and maintained with DMEM under 37 C, 5% CO2 for a day. For the cell shearing, we used CO2-independent media (Invitrogen) with growth factors (CC-4176, Lonza), and the oscillator temperature was maintained at 361 C. Cell images were acquired every 2 h. The program MetaMorph (Molecular Devices) was used for image acquisition, and the program ImageJ (NIH) was used to measure circularity and angle of orientation.

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Acknowledgements

This work was supported by NIH (GM 096040), Institutional Program for Young Researcher Overseas Visits, Japan Society for the Promotion of Science, Basic Science

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Research Program through the National Research Foundation of Korea (2014038270) and the Converging Research Center Program (2014048778) funded by the Ministry of Science, ICT & Future Planning. S.C.L.-P. thanks the NSF (DGE 1256260) for a graduate research fellowship. We thank Mark Burns, Brian Johnson, Lurie Nanofabrication facility and WIMS2 for microfabrication facilities and assistance. We thank the referees for very helpful suggestions.

Author contributions

S.-J.K. conceived, fabricated devices and performed the device experiments. S.T. supervised and guided the work. S.-J.K., R.Y. and S.C.L.-P. performed cell experiments. S.-J.K. and S.T. wrote and S.C.L.-P. edited the manuscript.

Additional information

Supplementary Information accompanies this paper at http://www.nature.com/naturecommunications

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Competing nancial interests: The authors declare no competing nancial interests.

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How to cite this article: Kim, S.-J. et al. Multiple independent autonomous hydraulic oscillators driven by a common gravity head. Nat. Commun. 6:7301 doi: 10.1038/ncomms8301 (2015).

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