# Predictable Duty Cycle Modulation through Coupled Pairing of Syringes with Microfluidic Oscillators

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## Abstract

**:**

## 1. Introduction

## 2. Working Principle

_{G}

_{1}); preventing the downward deflection of the membrane, and consequently preventing valve 1 from transitioning to an open position while P

_{G}

_{1}exceeds the source pressure of valve 1 (P

_{S}

_{1}) generated by the accumulation of fluid in the portion of the valve upstream from the valve 1 gate.

_{S}

_{1}has surpassed the sum of P

_{G}

_{1}and the inherent pressure threshold of valve 1 (P

_{th}

_{1}), determined by the specific mechanical properties of the membrane, the membrane is deflected downward, and fluid is allowed to travel through valve 1. A portion of this outflow is then diverted from its drain terminal to the gate terminal of valve 2, as the outflow from valve 1 had been diverted previously, and supplies the gate pressure necessary to force the accumulation of fluid upstream of valve 2, until the difference between P

_{S}

_{2}and P

_{G}

_{2}has exceeded P

_{th}

_{2}(Figure 1a,b). The coordination of these processes, resulting in the anti-synchronized opening and closing of both valve units, produces an oscillatory outflow (described in greater detail in previous work [2,21]).

**Figure 1.**Schematic for the experimental system. The three panels displayed represent the behavior of the microfluidic oscillator at three time points during operation under symmetric flow conditions. (

**a**) Two fluids (blue and red) are introduced through two syringes mounted on a single syringe pump. The fluids enter the device at a constant rate, but are converted into an oscillatory outflow when passing through the valves. (

**b**) A cross section of each valve unit at the time points displayed in panel (

**a**). Initially, the source pressure (P

_{S}

_{1}) is insufficient (P

_{S}

_{1}< P

_{G}

_{1}+ P

_{th}

_{1}) to displace the membrane downward, allowing the blue fluid to outflow. When the pressure has reached its maximum value (P

_{max}), the membrane is displaced (P

_{S}

_{1}> P

_{G}

_{1}+ P

_{th}

_{1}), allowing the red fluid to outflow until sufficient source pressure (P

_{S}

_{2}) has accumulated within the chamber above the opposite membrane (P

_{S}

_{2}> P

_{G}

_{2}+ P

_{th}

_{2}) allowing the blue fluid to outflow. (

**c**) The time points within the pressure data time series corresponding to the valve and outflow profiles presented in panels (

**a**) and (

**b**) are indicated. A sample P

_{max}and P

_{th}are also represented, as well as the relationship between inflow rate (Q

_{i}), internal capacitance (C

_{i}), and external capacitance (C

_{e}).

_{in}, C and P represent inflow rate, fluidic capacitance, and pressure respectively, may be expanded to describe the threshold-dependent mechanism underlying the functionality of the valves. Conceptually, the transition between a closed-to-open or open-to-closed valve-state is governed by the values of P

_{th}and P

_{G}set by the mechanical properties of the membrane and buildup of fluid pressure below the membrane (Figure 1b), respectively, and the rate at which fluid pressure builds within the valve region above the membrane (P

_{S}) [2]. The relationship between inflow rate and capacitance, thus, may be used to determine duty cycle as a function of time:

_{1}≅ Q

_{2}, where the mechanical properties of the membrane and valve compartments are preserved across both valves, the assumption is P

_{th}

_{1}≅ P

_{th}

_{2}and C

_{1}≅ C

_{2}, allowing us to consequently define duty cycle solely as a function of volumetric flow rate.

_{i}, would produce asymmetric duty cycles. However, in asymmetric conditions where Q

_{1}≠ Q

_{2}(e.g., Q

_{1}< Q

_{2}), the syringe supplying the greater volumetric inflow (Q

_{2}) will result in a greater threshold pressure for the valve regulating the lesser volumetric inflow, and consequently, P

_{th}

_{1}> P

_{th}

_{2}. The presence of this asymmetry suggests that the use of two identical syringes, evacuated at asymmetric linear velocities, would rely upon a complex balance between Q

_{in}, C, and P such that the duty cycles produced may not be accurately modeled by Equation (4). One way to maintain the relationship shown in Equation (4) would be to modulate C

_{i}together with Q

_{i}so that P

_{thi}× C

_{i}≈ constant. One way to achieve this conveniently is by mounting two plastic syringes of different cross-sectional area on one syringe pump (Figure 2), and utilizing the compliance of the syringe components [23] and resulting capacitive differences of the syringes [12]. Within the described system, as syringe outflow rate is a function of velocity and syringe cross-sectional area, and as both syringes are evacuated at the same linear velocity, we may further refine our definition of duty cycle as being a function of syringe diameter (Figure 2b). By using syringes of different diameters, we apply Equation (4) and demonstrate predictability of duty cycle values as a function of the combination of syringes used (Table 1).

**Figure 2.**Schematic for the experimental generation of symmetric and asymmetric volumetric flow rates, and changes in duty cycle and pressure profile produced as a function of syringe diameter. (

**a**) Two sample conditions where Syringe 1, (red), and Syringe 2, (blue), are mounted on a single syringe pump. The ratios illustrated are the symmetric 3 mL:3 mL (upper) and asymmetric 3 mL:60 mL (lower). Within the experimental protocol , Syringe 1 was held constant in all pairings while Syringe 2 was varied to achieve symmetric (50%) and asymmetric (>50%) duty cycles; and total volumetric inflow rate remained constant. Experimentally generated pressure profile waveforms are presented against alternating background bands representing the fluid outflow profile. (

**b**) Pressure profile and stimulation period for the four inflow ratio regimes. Pressure profiles were generated while the syringe pump was moving at a constant linear velocity such that the total volumetric inflow rate (the sum of the inflows supplied by each syringe) was maintained at a volumetric flow rate of 20 μL/min. The pressure profiles recorded (P) are presented above each trace representing the concentration of a fluidic stimulant ([S]) provided via Syringe 2, in the outflow.

## 3. Materials and Methods

#### 3.1. Master Mold Fabrication

#### 3.2. Microfluidic Oscillator Fabrication

#### 3.3. Microfluidic Oscillator Testing and Data Processing

_{2}≥ Q

_{1}and Q

_{2}+ Q

_{1}= Q

_{total}.

## 4. Results and Discussion

#### 4.1. Predictive Duty Cycle Control

**Table 1.**Different syringe pairings on a single syringe pump enables different duty cycles to be achieved, while maintaining a constant total volumetric inflow rate of 20 μL/min.

Syringe 1 | Syringe 2 | Duty Cycle (Expected) | Duty Cycle (Observed) | ||||
---|---|---|---|---|---|---|---|

Volume (mL) | Diameter (mm) | Inflow Rate (μL/min) | Volume (mL) | Diameter (mm) | Inflow Rate (μL/min) | ||

3 | 8.66 | 15.33 | 1 | 4.78 | 4.67 | 23.35% | - |

3 | 8.66 | 10.00 | 3 | 8.66 | 10.00 | 50.00% | 48.71% |

3 | 8.66 | 6.80 | 5 | 12.06 | 13.20 | 65.98% | - |

3 | 8.66 | 5.26 | 10 | 14.5 | 14.74 | 73.71% | 74.59% |

3 | 8.66 | 3.40 | 20 | 19.13 | 16.60 | 82.99% | - |

3 | 8.66 | 2.75 | 30 | 21.7 | 17.25 | 86.26% | 86.00% |

3 | 8.66 | 1.90 | 60 | 26.7 | 18.10 | 90.48% | 90.82% |

3 | 8.66 | 0.97 | 140 | 38.4 | 19.03 | 95.16% | - |

**Figure 3.**Experimental duty cycles overlap predicted values; flow rate ratio manipulation stably and reproducibly regulates duty cycle across multiple devices. (

**a**) Filled symbols represent duty cycle values observed and averaged across four syringe combinations and at five different total volumetric inflow rates. Unfilled blue circles represent predicted duty cycle values. All values are derived from time series data containing >6 oscillations. Duty cycle values are plotted against the squared ratio between syringe diameter (Syringe 2:Syringe 1) to illustrate the general trend observed. (

**b**) Duty cycle data collected from multiple devices (n = 3) is presented against the squared ratio between syringe diameter (Syringe 2:Syringe 1). Filled symbols represent duty cycle values recorded and averaged across four syringe combinations for total volumetric inflow rates ranging from 5 to 40 μL/min. Unfilled circles represent theoretical (predicted) duty cycle values. All averaged values are derived from time series data containing >6 oscillations. Error bars represent the calculated standard deviation for all duty cycle values recorded from each of three devices for all tested inflow rate ranges.

#### 4.2. Mounting Syringes on Separate Syringe Pumps Produces Unstable Duty Cycles

**Figure 4.**Single syringe pump setup results in more robust duty cycle control than two pump setup. A minimum of 7 sequential oscillations were observed using two experimental setups (either comprised of a multiple syringes mounted upon a single pump or single syringes mounted upon multiple pumps) to identify reproducibility and consistency of duty cycle. The data presented was acquired using both experimental setups at a total volumetric inflow rate of 20 μL/min. Error bars represent the 95% confidence intervals for experimentally observed results. Two different syringe pump models were utilized in the multiple syringe pump setup.

_{th}, but not in C; necessary for performing the reduction yielding Equation (4), and consequently, for the simplified and accurate prediction of duty cycle. The source of the observed instability at a specific flow rate ratio may be multifaceted; deriving from differences in manufacturing of the pumps themselves, differences in their calibration or age, and general unsteadiness inherently observed in syringe pumps [22,26]. As the presence of variability between syringe pumps is unavoidable, the use of multiple syringe pumps presents an inherent risk that predictability of the resulting duty cycle will be adversely effected due to an uncoupling between the pump-derived variability experienced by each individual syringe. Mounting multiple syringes upon a single syringe pump, however, ensures that each syringe experiences similar pump-derived variability. This coupling then ensures that slight instabilities in linear output are experienced simultaneously by both syringes; resulting in a predictable and stable duty cycle.

#### 4.3. Maximum Pressure Profile Remains Relatively Constant

_{th}values observed, even under extreme asymmetric conditions ($\left|{P}_{th1}-{P}_{th2}\right|<2$ kPa), are far below those reported in previous work ($\left|{P}_{th1}-{P}_{th2}\right|<55$ kPa) utilizing asymmetric valve units [8].

_{max}values recorded for each valve under the examined flow conditions are equivalent under symmetric volumetric inflow rates, but diverge from these values as the asymmetry between the two inflow rates is increased (Table 2).

_{max}); the initial outflow velocity from each valve is higher (Q

_{max}) relative to the stabilized baseline velocity subsequently achieved [24]. The lower P

_{max}values observed within this system, relative to values previously-reported [2], suggests a reduction in Q

_{max}and, thus, in the magnitude of the transient fluctuation in flow velocity accompanying the transition of each valve from a closed-to-open state. Despite this reduction, as fluidic shear is known to influence the morphological and phenotypical properties of cultured cells and tissues, the mere presence of this fluctuation may nonetheless represent a parameter which must be considered when utilizing this device for the performance of biological analyses.

_{max}values across both valves in one device demonstrates P

_{max}values for valve 1 increase relative to P

_{max}values for valve 2 in proportion to the degree of asymmetry between the inflow rate ratios across the two valves. All data presented is derived from one device, as inter-device variability led to differing absolute P

_{max}values across devices. Similar trends, however, were observed across all devices examined.

Total Volumetric Inflow Rate (μL/min) | 3 mL:3 mL | 3 mL:10 mL | 3 mL:30 mL | 3 mL:60 mL | ||||
---|---|---|---|---|---|---|---|---|

Valve 1 (kPa) | Valve 2 (kPa) | Valve 1 (kPa) | Valve 2 (kPa) | Valve 1 (kPa) | Valve 2 (kPa) | Valve 1 (kPa) | Valve 2 (kPa) | |

20 | 3.30 | 3.34 | 3.49 | 3.32 | 3.51 | 2.76 | 3.67 | 3.04 |

25 | 4.08 | 4.16 | 4.20 | 4.01 | 4.28 | 3.48 | 4.53 | 3.80 |

30 | 4.77 | 4.92 | 5.03 | 4.83 | 5.20 | 4.28 | 5.44 | 4.58 |

35 | 5.52 | 5.70 | 5.72 | 5.54 | 6.11 | 5.08 | 6.34 | 5.35 |

40 | 6.31 | 6.52 | 6.52 | 6.29 | 6.98 | 5.86 | 7.18 | 5.94 |

#### 4.4. Syringe Properties Influence Capacitance

_{th}observed under asymmetric inflow rates (described in greater detail below).

**Figure 5.**Fluidic capacitance increases significantly with increasing syringe volume. Capacitance values were averaged for individual syringes using data collected at multiple volumetric flow rates (ranging from 10 to 40 μL/min). All values are derived from time series data containing >6 oscillations, with five replicates (p < 0.0002). Error bars represent the 95% confidence intervals of all capacitance values obtain over multiple inflow rate ranges.

#### 4.5. Different Asymmetric Inflow Rates at Constant Total Volumetric Inflow Rate Produce Distinct Periods

_{th}using experimental data collected under multiple inflow conditions. We found that under asymmetric flow regimes, P

_{th}and C exhibit an inverse relationship, where P

_{th}is higher for the valve experiencing the lower flow rate (valve 1), lower for the valve experiencing the higher flow rate (valve 2) and where the absolute difference between P

_{th}(i.e., $\left|{P}_{\text{th}1}-{P}_{\text{th}2}\right|$) increases with the degree of asymmetry between the syringes used. As C is proportional to the size of a given syringe, it is consequently proportional to Q

_{in}, which increases with the size of the syringe used. This finding is in agreement with previous results reported for four-way valves, where an increase in volumetric inflow rate through one valve increases calculated P

_{th}for the opposite valve [21].

_{th}in conditions with lower Q

_{in}, will produce higher t

_{off}; and that as the asymmetry between the flow rate across each valve increases, t

_{off}will increase for the valve with a lower inflow rate, producing larger oscillation periods.

_{th}and C for each respective syringe pairing, we approximated t

_{off}for both valves. We then compared the calculated period approximation with experimental data (Figure 6), and observed that the relationship between volumetric flow rate and period is preserved. We limited the presented period data to one device, as all devices tested exhibited similar trends, with slight variations in absolute values. Such variations may originate from differences in device size (e.g., thickness of the PDMS membrane), fabrication procedure or material batch characteristics. In addition, larger standard deviations in the period, prominent at greater asymmetric inflow rates, may also originate from fluctuations in syringe pump pressure [26].

_{th}, but not in C, introducing a source of complexity to the relationship between volumetric flow rate ratio and duty cycle. Practically, this would result in the inability to reduce down to Equation (4). However, by utilizing syringes of differing diameter, volumetric flow rate-dependent changes in P

_{th}are counteracted, allowing one to perform straightforward prediction of duty cycle as a function of volumetric flow rate ratio.

**Figure 6.**Asymmetric inflow rates produce markedly different periodicity, yet can be estimated relatively-well. Observed period values for each syringe combination demonstrate the range of periodicities generated for each of the four combinations tested. The estimated oscillatory period was calculated by applying Equation (5) for each syringe combination; values for C and P

_{th}were derived from the minimal and maximal volumetric inflow rates tested, and were used to establish a linear relationship for P

_{th−i}where P

_{th−i}= m × Q

_{i}+ b. Predicted period values (unfilled) were then compared to the averaged measured period values (filled). All values are derived from time series data containing >12 oscillations, and error bars represent 95% confidence intervals for experimentally observed results.

#### 4.6. Estimating Rest and Stimulation Pulse Duration for Control of Rhythmic Stimulation

_{th}for each valve must be measured with respect to its corresponding syringe and input Q

_{i}values, respectively. Measurements of P

_{th}for each valve must be conducted at two total volumetric inflow rates (we used 5 μL/min and 40 μL/min, the minimal and maximal total volumetric inflow rates, respectively) to approximate the linear relationship P

_{th−i}= m × Q

_{i}+ b. This relationship may then be used to approximate intermediate P

_{th−i}values for different inflow rates, and for each syringe pairing. The P

_{th−i}, C, and Q

_{i}values may then be used, in equation (5), to determine the off-time for each valve. The sum of the off-times will estimate the periodicity of the device for a given syringe combination. By this method, a curve in general agreement with empirical data, and representing the periodicity as a function of the ratio between syringe diameters, may be generated (Figure 6). This curve may then be utilized to identify an appropriate total volumetric inflow to produce a desired D and R for the specific syringe combination being used. Conversely, this curve may also be utilized to identify the appropriate combination of syringes necessary to modify the length of D or R.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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## Share and Cite

**MDPI and ACS Style**

Lesher-Perez, S.C.; Weerappuli, P.; Kim, S.-J.; Zhang, C.; Takayama, S. Predictable Duty Cycle Modulation through Coupled Pairing of Syringes with Microfluidic Oscillators. *Micromachines* **2014**, *5*, 1254-1269.
https://doi.org/10.3390/mi5041254

**AMA Style**

Lesher-Perez SC, Weerappuli P, Kim S-J, Zhang C, Takayama S. Predictable Duty Cycle Modulation through Coupled Pairing of Syringes with Microfluidic Oscillators. *Micromachines*. 2014; 5(4):1254-1269.
https://doi.org/10.3390/mi5041254

**Chicago/Turabian Style**

Lesher-Perez, Sasha Cai, Priyan Weerappuli, Sung-Jin Kim, Chao Zhang, and Shuichi Takayama. 2014. "Predictable Duty Cycle Modulation through Coupled Pairing of Syringes with Microfluidic Oscillators" *Micromachines* 5, no. 4: 1254-1269.
https://doi.org/10.3390/mi5041254