An electrically-controlled programmable microfluidic concentration waveform generator
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Biological systems have complicated environmental conditions that vary both spatially and temporally. It becomes necessary to impose time-varying soluble factor concentrations to study such systems, including cellular responses to pharmaceuticals, inflammation with waxing and waning cytokine concentrations, as well as circadian rhythms and their metabolic manifestations. There is therefore a need for platforms that can achieve time-varying concentrations with arbitrary waveforms.
To address this need, we developed a microfluidic system that can deliver concentration waveforms in a fast and accurate manner by adopting concepts and tools from electrical engineering and fluid mechanics. Specifically, we employed pulse width modulation (PWM), a commonly used method for generating analog signals from digital sources. We implement this technique using three microfluidic components via laser ablation prototyping: low-pass filter (lower frequency signals permitted, high frequency signals blocked), resistor, and mixer. Each microfluidic component was individually studied and iteratively tuned to generate desired concentration waveforms with high accuracy. Using fluorescein as a small-molecule soluble factor surrogate, we demonstrated a series of concentration waveforms, including square, sawtooth, sinusoidal, and triangle waves with frequencies ranging from 100 mHz to 400 mHz.
We reported the fabrication and characterization of microfluidic platform that can generate time-varying concentrations of fluorescein with arbitrary waveforms. We envision that this platform will enable a wide range of biological studies, where time-varying soluble factor concentrations play a critical role. In addition, the technology is expected to assist in the development of biomedical devices that allow precise dosing of pharmaceuticals for enhanced therapeutic efficacy and reduced toxicity.
KeywordsConcentration waveform Pulse width modulation Microfluidics Time-varying soluble factors
Differential interference contrast
Pulse width modulation
standard cubic centimeters per minute
Time-varying concentrations of soluble factors play an essential role in proper functioning of living systems. A well-known example of this is insulin. While cells respond to spikes of insulin concentration in blood by increasing cellular uptake of glucose, steady-levels of insulin desensitize cells and reduce glucose uptake . There is also a large interest in studying how dynamic extracellular signals can be transduced into intracellular signals and give rise to emergent properties [2, 3]. Furthermore, an expanding body of research reveals the importance of circadian rhythms on inflammation and metabolism [4, 5]. In order to model these complex dynamic biological processes, there is a need for sensors and actuators that can monitor and deliver time-varying concentrations of soluble factors . Even though both the sensor and actuator components are equally important, the focus here is the latter and progress on the former can be found elsewhere [7, 8, 9]. One way to categorize the waveform generators is with respect to their concentration pattern output, namely: digital concentration waveforms (i.e., binary/pulsatile switching, which may be relevant for modeling insulin delivery ) and analog concentration waveforms (i.e., continuous manipulation of the amplitude and/or frequency, which may be relevant for cytokine patterns following injury ). To generate a digital concentration waveform, the general approach is based on switching between two or more liquid inlets, analogous to a multiplexer in electronics, such as peristaltic pumps , acoustically vibrating bubbles , and magnetic stir rods , as well as passive mixers including serpentine channels and herringbone structures [15, 16]. A shortcoming to these approaches is their slow and unpredictable temporal response. Moreover, these designs greatly limit the application that it is only able to create time-varying concentration pulses rather than dynamically changing concentration waveforms. In order to deliver smoothly-varying concentration waveforms, different methods have been devised, including flow control via gas-pressure gated valve and pulse width modulation. However, the improved control of concentration waveforms has come with the expense of system complexity such as gas pipeline, fluid channel network array, many inlets/outlets structure and waste outlets to avoid flow interruptions . We envision that a scalable platform that can deliver concentration waveforms that can be customized by the user would provide an avenue to study complex biological processes. To that end, we developed a microfluidic system that can modulate the concentration waveforms in a fast and accurate manner via pulse width modulation (PWM) that was controlled by electrical signals.
Results and discussion
Microfluidic system integration
The electronic-hydraulic analogy allows for applying this electrical concept to fluidics (Additional file 1: Figure S1), as discussed elsewhere [20, 21]. Briefly, a fluidic resistor is a microfluidic channel with specific dimensions to restrict fluid flow while a fluidic capacitor is a chamber with a flexible membrane that can store liquid scaled with respect to the liquid pressure . The proposed microfluidics concentration waveform generator system utilizes three different microfluidic chips (Fig. 1b): (i) filter chip, (ii) resistor chip and (iii) mixer chip. The filter chip consists of an elastic membrane-capped cavity as the capacitor and a serpentine channel as the resistor. The resistor chip contains a serpentine channel design and the mixer chip contains a simple Y-shape channel design. The digitization of the desired output signal (generation of the pulse train with specific pulse widths, that is, pulse width modulation) is performed using a MATLAB algorithm (shown in Supporting Information). The pulse train is then applied through a set of high-current switches (Maxim Integrated) to control the flow selection valve. As shown in Fig. 1b, solutions containing molecules of interest with the same concentration are kept in two reservoirs that are labeled as the high-pressure analyte reservoir and low-pressure analyte reservoir (shown in yellow). These two reservoirs are connected through a selection valve to the inlet of the filter chip and placed at different heights in order to generate different hydrostatic pressures. When the flow selection valve is controlled to switch between these two solutions, even though the concentrations of these two solutions are the same, the output instantaneous flow rates are different, which leads to different volumes of the solution flowing into the filter chip per unit time. The filter chip then acts as a low-pass filter to attenuate the high frequency components originating from the PWM signal and produce an analog output signal of flow rate proportional to the time average of each pulse.
A reservoir filled with the buffer (shown in blue) is connected to the inlet of the resistor chip through an adjustable stop valve that allows the flexibility to manually switch out the solution. The buffer from the resistor chip is used to generate different waveforms by controllably diluting the solution from the filter chip and the final mixing of the solution with the desired concentration waveform is achieved on the mixer chip. A syringe pump is connected to the outlet of the mixer chip and withdrawing the liquid at a constant rate. Thus, the final mixed solution in the mixer chip is at a steady flow rate with the pre-programmed (via PWM pulse train) concentration waveform. Maintaining a constant flow rate while varying the concentration of the solution is not trivial, yet extremely important since in biological experiments the flow rate can influence adherent cell response via hydrodynamic shear forces . Put another way, as solutions from filter chip and resistor chip enter the mixer chip together, the sum of the individual flow rate out of filter chip and resistor chip equals to the final flow rate in the mixer chip, which is a constant number programmed by the syringe pump. In order to generate an even flow split between the analyte and buffer on the mixer chip at the low-concentration state (flow selection valve not controlled), the microfluidic channel resistance between the resistor chip and filter chip as well as the hydrostatic pressure of the liquid between main analyte reservoir and buffer reservoir are the same. Therefore, the main analyte reservoir and buffer reservoir were placed at same height. Taking sinusoidal concentration waveform as an example, desired concentration waveform, the concentration and flow rate profiles with respect to time at four different nodes (i: entering filter chip; ii: leaving filter chip and entering mixer chip; iii: entering resistor chip; iv: leaving mixer chip) are shown inside the box in Fig. 1b. These three microfluidics chips in the system can be individually optimized, allowing for improving the overall system performance. The experimental setup of the entire system can be seen in Additional file 1: Figure S2 in supporting information (SI).
In order to facilitate the characterization of the system, we used fluorescein (a small-molecule drug surrogate) for the analyte and deionized (DI) water for the buffer throughout the experiments to allow monitoring the concentration variations with high spatial and temporal resolution. An inverted fluorescence microscope was used to record a short time-lapse video or capture a series of images. The images or the video frames were then uploaded to ImageJ (NIH freeware for image analysis) and the corresponding fluorescence intensity was converted into a gray-scale value and was plotted via MATLAB for post-data analysis (script shown in SI).
Filter Chip characterization
The filter chip is used for producing an analog output waveform by removing high-frequency components of the PWM waveform resulting from the bimodal flow selection valve. In designing the filter chip, we utilized a first-order resistor-capacitor (RC) low-pass filter (LPF), which consisted of the microfluidic channel as the resistor and a silicone membrane-capped cavity as the capacitor, as reported elsewhere [22, 24]. We used an elastomer, polydimethylsiloxane (PDMS), as the membrane material and a thin PDMS membrane was bonded on a glass slide covering a cavity hole to form a capacitor. The resistance was controlled by changing the channel dimensions, while the capacitance was adjusted by varying the diameter of the membrane. The fabricated filter chip can be seen in Additional file 1: Figure S4 and the cross-sectional schematic can be seen in Additional file 1: Figure S3b in the supporting information. In order to minimize the influence of parasitic capacitances (due to mechanically-compliant components) on the performance of the filter chip, rigid glass was used as the substrate and rigid polyetheretherketone (PEEK) tubing was used for connections.
The experimentally-measured parameters of the three low-pass filter chips
Designed Diameter D0 (mm)
Experimental Time Constant τ (sec)
Experimental Cut-off Frequencies fc (Hz)
Experimental Capacitance C (m3/Pa)
1.449 × 10−14
1.693 × 10−14
2.150 × 10−14
Mixer Chip characterization
The fluorescein solutions from high-pressure analyte reservoir and low-pressure analyte reservoir were controlled by the selection valve to flow into the filter chip and mix with the DI water from the resistor chip. The final mixed solution with the desired fluorescein concentration waveform was eventually achieved on the mixer chip. The mixing efficiency of the mixer chip determines how fast (i.e., within less channel length) the desired concentration waveform can be obtained.
We first characterized and evaluated the herringbone mixer to study the mixing efficiency with different numbers of pattern repetitions. Each number of pattern repetitions (also referred to as cycle) of the herringbone structure is 2.3 mm long and five different chips with five unique numbers (one through five) were tested. As it can be seen from the distribution of fluorescein concentration across the channel width (Fig. 3c), the Y-channel control (at the Y-channel junction) is highly ineffective at creating a uniform concentration along the channel width, as confirmed by the FWHM analysis (Additional file 1: Figure S6). This is also apparent as the width of high fluorescence intensity region (high concentration of fluorescein) after the junction is roughly the half of the entire channel width (Fig. 3c), indicating that the two solutions were not mixed thoroughly. The inclusion of herringbone mixer patterns improved mixing efficiency due to the circular vortexes that accompany the off-center grooves . Since there was no significant improvement in the mixing efficiency for the herringbone structures for more than three-pattern repetitions (as shown in Additional file 1: Figure S6), the three-pattern repetition architecture was chosen. Obstacle mixer, albeit a much longer channel (38.3 mm), also enabled robust mixing (Additional file 1: Figure S6). For this design, the negative obstacle angles create chaotic flow by manipulating flow towards the center of the channel and lead to effective mixing . While the obstacle mixer exhibited more uniform mixing than the herringbone mixer along the width of the channel, this was at the expense of a significantly longer time (~ 5 times longer channel), which may be impractical for chip lay-out. In contrast, plain channels (without any mixer patterns) with equivalent lengths to the three-pattern herringbone mixer and the obstacle mixer (shown respectively as Equiv YHM L and Equiv YOM L in Fig. 3d and Additional file 1: Figure S6) displayed poor mixing due to the purely diffusive mixing mechanism available. As the outcome of the mixer chip characterization, three-pattern cycle version of the herringbone mixer was chosen as the final mixer chip component.
An important characteristic of mixers is that they can also be characterized as low-pass filters that attenuate high-frequency waveforms and do not affect low-frequency waveforms. While this further smooths out the output signal (waveforms at nodes “ii” and “iv” in Fig. 1b), it may lead to smearing of the waveform. This becomes more significant for longer mixing times (e.g., longer mixer channels, such as the YOM), since dispersion (due to diffusion along the channel length) further broadens the concentration waveforms and reduces the peak concentrations . The detailed discussion and its mathematical treatment can be found in the supporting information. The time response and frequency response of herringbone mixer and obstacle mixer is shown in Additional file 1: Figure S7.
Concentration waveform generation
In the current microfluidic system, the cut-off frequencies of the filter chip are between 200 mHz and 500 mHz whereas the mixer chip are between 15 mHz and 70 mHz. The mixer chip limits the speed of the final concentration waveform as it has a significantly lower cut-off frequency than any of the filters. However, the channel length correlates with the cut-off frequency, thus a shorter mixer chip can be used for faster response. Depending on the application and the desired waveform’s characteristic, different filters and mixers could be tuned easily to obtain very specific concentration waveforms.
We presented a microfluidic concentration waveform generator by adopting techniques and tools from electrical engineering and fluid mechanics. Specifically, we employed pulse width modulation (PWM) technique enabled by an electrically-controlled flow-selection valve to create flow-rate pulses of a high concentration analyte that were smoothed out by a fluidic first-order low-pass filter before titrating it into a buffer solution at a Y-channel junction, and mixing it via a microtextured channel. Each component was separately characterized before implementation into the system. The system successfully generated fundamental waveforms (e.g., sinusoidal, triangle, sawtooth, square) and a MATLAB algorithm was developed to program more complex arbitrary waveforms.
Having established a system that can create arbitrary concentration waveforms, it is important to conclude by discussing its utility in biology. Biological processes are inherently a product of sophisticated negative and positive feedback loops with different time scales (e.g., phosphorylation versus synthesis of proteins). Per system identification theory , in order to deconvolve these mechanisms with different time scales, it is necessary to develop tools that can characterize the biological system’s response to soluble factors with different magnitudes and temporal profiles. An emerging area of relevance is the cross-talk between inflammation and metabolism, where cytokines influence metabolic processes (e.g., tumor necrosis factor-alpha and PPAR interaction ), which may lead to paradoxical effects like hypermetabolism in cancer and obesity, both of which has an inflammatory component. It is well-documented that cytokines and their temporal response play a significant role in physiological time course following injury and in a large set of diseases [30, 31]. From a more applied perspective, other examples of this phenomenon are widespread in biology such as the tolerance effect exhibited by various drug administrations in which down-regulation of receptor expression can blunt the effect of a drug if the initial dose is given at too high level, or at too rapid of an interval between doses [32, 33]. For a such case, drug dosing at the correct waveform may improve efficacy. Concentration waveforms can also be tuned into a more repeatable pattern to study the circadian rhythms and their influences on inflammation and metabolism in many diseases including atherosclerosis and obesity [4, 5]. Progress in such studies can be translated into pharmacological and/or nutritional interventions with tremendous therapeutic potential. Overall, we expect that the engineered platform will enable a rich set of studies ranging from fundamental biology to translational medicine.
Flow selection valve and pulse width modulation (PWM) signal generation
The flow selection valve is the essential component in the waveform generator system and it controls the flow-rate alternation between the liquid in high-pressure analyte reservoir (higher hydrostatic pressure) and low-pressure analyte reservoir (lower hydrostatic pressure) to flow into the filter chip. It is electrically-controlled, where in order to toggle between the high-pressure analyte reservoir and low-pressure analyte reservoir, 12 V was applied on only one side and then switched to the other. A pair of high-current switches was used to convert logic signals (PWM pulse train) into 12 V lines to change the state of the valves. The PWM signals for the waveforms of interest were generated by a custom MATLAB algorithm (shown in Supporting Information). The PWM signal was imported into the Analog Discovery’s waveform generator and directly used to control the flow selection valve through switches. This script (see supporting information) can generate sinusoidal, square, and sawtooth waveforms but can easily be adapted for any waveform.
Channel resistance measurement by gravity induced flow
Microfluidic Chip fabrication
The specific channel depth and width vary for each chip. In the mixer chip, the channel depth and width are 200 μm. The filter and resistor chips have a smaller channel depth and width of 100 μm, as a much higher resistance is needed for the two chips to produce fast waveforms. The channel depths and widths were measured by a profilometer and confirmed via a differential interference contrast (DIC) optical microscope. Subsequently, NanoPort connectors (Western Analytical Products) were glued onto the inlets and outlets of the microfluidic chips for tubing connection.
Data analysis for time and frequency responses
The time and frequency responses were analyzed for the filter chip and resistor chip. For determining the time-constant and cut-off frequency, MATLAB algorithms were used. Briefly, MATLAB was used to separate a full waveform into equivalent sections and average them to accurately find step and frequency responses. Subsequent analysis was completed on the short output waveforms obtained from this script (see supporting information) instead of the full waveforms. This script finds the first period of a waveform and uses it as a template in cross-correlation with the entire waveform. The highest values obtained from cross-correlation are the more-closely-matched sections of the waveform to the template. Each section is then averaged together to find the step and frequency response. Detailed information about the MATLAB code can be found in the supporting information.
Overall system evaluation and characterization
Fluorescein solution and deionized water were used in the system to demonstrate the generation of programmed concentration waveforms. As the fluorescein solution appears bright and the deionized water appears dark under an inverted fluorescence microscope (Zeiss Observer D1), the intensity of the liquid inside the channel can be directly correlated to the actual concentration of fluorescein via a calibration curve. The fluorescence microscope was used to record a short time-lapse video or capture a series of images. Each video sample or the image sample was then uploaded to ImageJ and the corresponding brightness was extracted into a gray value and then was plotted through MATLAB for post-data analysis, including the full-width at half-maximum extraction (Additional file 1: Figure S6).
We gratefully acknowledge support from National Science Foundation (NSF) awards [CBET-1512745 and CBET&DMR-1454426] and National Institutes of Health (NIH) NIBIB Trailblazer award [R21 EB024635]. The funding from all entities listed were used for expenses associated with the experiments and data analysis. ZL and ES were partially supported by NSF and NIH awards. JG and LW were partially supported by NSF awards.
Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
JG and ES conceived the project. JG, ZL, LW and ES designed the experiments. JG, ZL and LW performed the experiments and analyzed the results. JG, ZL, BP and ES wrote the manuscript and analyzed the results. All authors read and approved the final manuscript.
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