Scaling microfluidic throughput with flow-balanced manifolds to simply control devices with multiple inlets and outlets

Abstract

Microfluidics can bring unique functionalities to cell processing, but the small channel dimensions often limit the throughput for cell processing that prevents scaling necessary for key applications. While processing throughput can be improved by increasing cell concentration or flow rate, an excessive number or velocity of cells can result in device failure. Designing parallel channels can linearly increase the throughput by channel number, but for microfluidic devices with multiple inlets and outlets, the design of the channel architecture with parallel channels can result in intractable numbers of inlets and outlets. We demonstrate an approach to use multiple parallel channels for complex microfluidic designs that uses a second manifold layer to connect three inlets and five outlets per channel in a manner that balances flow properties through each channel. The flow balancing in the individual microfluidic channels was accomplished through a combination of analytical and finite element analysis modeling. Volumetric flow and cell flow velocity were measured in each multiplexed channel to validate these models. We demonstrate eight-channel operation of a label-free mechanical separation device that retains the accuracy of a single channel separation. Using the parallelized device and a model biomechanical cell system for sorting of cells based on their viability, we processed over 16 × 10⁶ cells total over three replicates at a rate of 5.3 × 10⁶ cells per hour. Thus, parallelization of complex microfluidics with a flow-balanced manifold system can enable higher throughput processing with the same number of inlet and outlet channels to control.

INTRODUCTION/BACKGROUND

Microfluidics can harness microscale physics to enable new processing capabilities. The precision of microscale fabrication is used to manipulate single cells with physical and chemical interactions for applications in cell separations,^1–4 transfections,^5–7 and various point-of-care diagnostics and treatment.^8,9 The scale of interactions ranges from single cell properties,^10–13 single-organism analysis,^14,15 and micro-cultures^16,17 that all rely on precise channel geometry and flow profile. Complex microfluidics have also been developed that use multiple inlets and outlets to separate cells, for example, through differences in mechanics that include stiffness, viscosity, adhesion, and size.^18–24

Small processing volumes that are inherent to microfluidic channels can result in fine manipulation on the single cell level, yet the dimensions of a single channel limit the rate of throughput to applications with small volumes in the diagnostics or research setting. Scaling to larger processing volumes is required for key applications, such as genomic analyses^25,26 or processing in a clinical setting.^27–29 Microfluidic platforms can be scaled by increasing the concentration of cells processed, increasing the fluid flow rate, or multiplexing the channels. Often, the first two approaches have upper bounds limited by the distortion of the physical phenomena being utilized in the microfluidic device operation [Fig. 1(a)].

FIG. 1.

Device parallelization allows for linear improvement of processing throughput: (a) throughput of microfluidic cell sorting devices is increased by increasing the cell density and flow velocity until the device effectiveness is diminished. At high cell densities, cell–cell interactions disrupt the translations of cells at each ridge. At high flow velocity, the hydrodynamic forces outweigh the normal forces associated with cell deformation at the ridges and cells are not deflected sufficiently. (b) Increasing the number of parallel channels in a device results in a linear improvement of processing throughput. This improvement requires all channels to be operated at the same flow conditions. (c) Design process for linearizing and parallelizing microfluidic stiffness-based sorting device for increased throughput.

Multiplexing can increase throughput linearly with the number of channels [Fig. 1(b)].^30–37 However, parallelization of device architectures that have more than a single inlet or outlet results in proportional increases in the number of ports. In previous studies, we have developed a sorting platform that relies on three inlets for flow focusing and five outlets for fractionation of cells.^10,11 This and other implementations have shown processing rates on the order of 10,³⁸ 20,³⁹ or 100 cells per second^3,40 or 1–10 ml/min of volume.¹⁰ The obvious approach of operating multiple separate devices simultaneously quickly reaches the limit of fluid handling and sample collection. Therefore, to parallelize complex channels for increased microfluidic output, we will develop an approach that simplifies the inlet and outlets in a manner that maintains identical flow parameters across the multiple channels.

In this manuscript, we describe a scalable approach for multiplexing complex microfluidics. Using two fluidic layers, we operate channels in one layer with aligned outlet ports that are combined using a second, manifold layer. This approach is generalizable and applicable to microfluidic platforms with multiple inlets or outlets. To minimize the total device footprint, we convert the inlets and outlets from a symmetric radial design to a linearized design [Fig. 1(c)]. The aligned outlets can interface with channels in a manifold layer that combines like-outlets and inlets from each individual device. Using first analytical modeling⁴¹ followed by fine tuning with finite element modeling,³⁶ the fluid flow is balanced to each inlet and outlet. The volumetric output of each channel is experimentally compared to verify commensurable operation to our single channel platform. This approach employs passive flow control to reduce 24 inlet ports and 40 outlet ports for eight channels to three inlet ports and five outlet ports. We demonstrate the ability to improve the throughput of microfluidic cell sorting by over 8-fold to over 5 × 10⁶ cells per hour while maintaining the accuracy of separation of a single channel.

EXPERIMENTAL METHODS

Modeling and analytical calculations

A key aspect of maintaining similar flow conditions for each parallel channel is to balance both outlet channel resistances and the manifold layer channel resistances to achieve equal fluid distribution and recombination rather than relying on matching both channel length and width. Fluid distribution networks for the linearized channel layer and the manifold layer were designed using an analytical flow resistance model. For a rectangular channel, Eqs. (1) and (2) describe the pressure drop, ΔP, and flow resistance, R, respectively, where Q is the volumetric flow rate, μ is the dynamic viscosity, L is the channel length, h is the channel height, and w is the channel width,

$$\mathrm{\Delta }P=R\times Q,$$ (1)

$$R={\displaystyle \frac{1}{1-0.63\left(\frac{h}{w}\right)}{\displaystyle \frac{12\mu L}{h^{3}w}.}}$$ (2)

Equation (2) assumes a high aspect ratio for the channel in which the channel width is substantially larger than the height. For the linearized devices, the outlet channel ratios ranged from 4:1 in the shorter channels to 20:1 in the longer channels. In the narrower channels, there is potential for over or under estimation of the channel resistance using this approach. To create the balanced channel designs, resistance of each outlet channel must be equal. By equating Eq. (2) for two channel geometries, the relationship of channel width and length can be expressed using Eq. (3), where L₁, L₂, w₁, and w₂ are the lengths and widths of two different outlet channels. The channel height, h, is constant across all channel geometries because the fabrication method requires the channel to maintain the same thickness,

$$w_1=0.63h\left(1-\frac{L_1}{L_2}\right)+w_2\left(\frac{L_1}{L_2}\right).$$ (3)

The microfluidic flow resistance equations were applied to both design the parallel channel layout as well as the manifold layer. In the parallelization process, Eq. (3) is used to set the channel widths for each outlet with a minimum channel width set at 100 μm. The manifold layout design process was more complex due to the variation in channel dimensions in the main supply arm, multiple connecting sections of different widths, and the connecting vias to the separation layer, as shown in the supplementary material (Fig. 1). The width of each channel section and number of downstream vias determine the flow resistance. Equation (4) shows a representative calculation of the pressure drop between the inlet port and a single via. In this equation, the pressure drop to any via is equal to the summation of the resistances between the via and inlet multiplied by the flow rate in each resistance segment. Similar equations were developed for each via of a manifold and a system of equations was established for each manifold. Excel's Solver tool was used to minimize the mean squared variance of pressure drop between vias, which ensured via flow rates were equal within and between the manifold paths. Thus, the flow rate would be matched from each inlet and outlet of each device,

$$\mathrm{\Delta }{P}_1=Q[R_1+2R_2+3R_3+4R_4+5R_5].$$ (4)

Finite element analysis (FEA) was performed to verify volumetric flow and make fine adjustments to account for error that could be introduced in the analytical method due to high-aspect ratio or other assumptions. A 2D mesh was formed in COMSOL based upon a computer aided design (CAD) of the channel layout and FEA was performed using the laminar flow package and an estimate of channel width. The flow rate to each outlet or manifold was calculated using the built-in integral function to sum velocity values over each outlet channel. The resulting flow rate measurements were used to adjust the channel designs and iteratively test the flow rates until the differences between channels were within 5% of the average value.

Microfluidic fabrication

SU-8 on silicon wafer molds for “tree” designs were created using previously described cleanroom techniques.⁴² The multiplexed microfluidic approach requires two PDMS layers. The first layer is the linearized and parallelized sorting channel. Like the “tree” design, this silicon mold has two layers: a gap layer and a channel layer. The new mold was made using reactive ion etching (RIE). A SC1827 or SC1813 photoresist (Microposit) was spun onto bare silicon wafers (University Wafer) depending on the etch depth required. The layer design was exposed using an MLA150 mask writer at 405 nm wavelength. The resist was developed with MF-319 (Microposit) and hard baked. The wafer went through a 30 s descum process using an HRM ICP plasma etcher (Surface Tech Sys) before etching with a Bosche process. The etch depth was measured using a stylus profilometer (P15, Tencore). The remaining resist was stripped in an acetone bath with sonication. The process was repeated for the second layer defining the sorting channel. A single etch step was used to create the second PDMS mold at a thickness of 75 μm. After the etching process was completed, each mold was exposed to Trichloro(1H,1H,2H,2H-perfluorooctyl)silane (Sigma-Aldrich) to form a hydrophobic surface on the silicon and assist with demolding cured polydimethylsiloxane (PDMS) . PDMS at a 10:1 ratio was used to mold both layers and bonding was done with a plasma cleaner (Harrick Plasma) using traditional soft-lithography techniques.⁴²

Cell culture

A HEY A8 ovarian cancer cell line that features a Cas9-GFP cassette was cultured in complete media consisting of RPMI-1640 (Sigma-Aldrich) supplemented with 10% v/v fetal bovine serum (Atlanta Biologicals) and 1% v/v penicillin-streptomycin (Sigma-Aldrich). Cells were cultured at 37 °C at 5% CO₂.

For the flow rate optimization experiments and high-speed video analysis, cells were prepared for processing by trypsinization and resuspension in a neutrally buoyant flow buffer [complete media, either 20% v/v Percoll (Sigma-Aldrich) or 10% v/v OptiPrep (Sigma-Aldrich) and 0.1% v/v Pluronic F-127 (Millipore Sigma) with 1 mg/ml DNAse I (Sigma-Aldrich) at approximately 1–2 million cells/ml]. Cells were strained using a 20 μm pore filter (PluriSelect) and loaded into a syringe (VWR) for microfluidic processing.

To validate biomechanical separation, we used a heat-treated cell viability model. Separate flasks of cells were first stained using 2 μM CellTracker Green CMFDA (ThermoFisher) and 500 nM Cell Tracker Deep Red (ThermoFisher) in serum-free media. Directly before microfluidic processing, cells were trypsinized and transferred to a conical tubes. A tube of red-dyed cells was placed in a water bath at 65 °C for 10 min to kill and stiffen the cells. Both the green- and red-dyed cells were resuspended in the flow buffer at 1–2 × 10⁶ cells per ml and strained through a 20 μm filter. Each sample was mixed at a 1:1 ratio so that the initial inlet population of cells would be approximately 50% red, dead, stiff cells and approximately 50% green, live, soft cells. In practice, initial population percentages ranged from 33% to 65% live cells and 28% to 60% dead cells as validated with flow cytometry. The prepared cell samples were loaded into a syringe for injection into the microfluidic chips using a vertically aligned syringe pump. For each single device trial, 2 confluent T75 flasks (VWR) of cells were prepared for processing (1 red, 1 green). For each multiplex device trial, 6 confluent T75 flasks were prepared for processing (3 red, 3 green).

AFM and force curve analysis

To confirm a stiffness difference between live and heat-treated cells, we used force spectroscopy to obtain force–indentation curves with an atomic force microscope⁴³ (Asylum Research) with an integrated optical microscope (Nikon). To improve the contact geometry, a 7.32 μm spherical polystyrene particle was attached to a tipless silica nitride cantilever (Bruker Probes) using a two-part epoxy (JB Weld). The cantilever was calibrated using the Sader method⁴⁴ to determine the deflection inverse optical lever sensitivity and spring constant and the measured stiffness constant was approximately 30 pN/nm.

Cells were seeded onto glass coverslips (Fisher Scientific) coated with 3.5 μg/cm² CellTak (Corning). For measurements, the cantilever probe was visually aligned with the cell center and moved with a velocity of 2 μm/s to indent the cell with increasing compressive force until a force trigger of 5 nN was reached. The cantilever was held in position for 10 s, dwelling toward the surface, to record viscous relaxation of the cell before retraction. We collected 50 cellular measurements per condition. We analyzed the force curves by applying the Hertzian contact model to calculate the cellular reduced Young's modulus using custom code written in R (https://github.com/nstone8/Rasylum).⁴⁵ The population measurements were compared using a t-test with a significance level of α = 0.05.

Microfluidic device cell separation

The microfluidic device was set up on the stage of an inverted optical microscope (Nikon) for monitoring of cell trajectories. High-speed videos of the cells were recorded using a Phantom camera at 2500–3000 frames per second to monitor cell trajectories and velocity after interactions with the diagonal ridges. Sheath fluid flow was controlled using two syringe pumps (Harvard Apparatus). Once the device was prepared, the syringe of cells in flow buffer with DNAse was connected to the cell inlet of the device with tubing using a third syringe pump. After sorting, the volume of fluid collected at each outlet was measured for comparison of volumetric flow output variability between outlets.

High-speed video analysis—Cell trajectories and cell velocity

To measure cell trajectories, ImageJ was used to extract an image stack from each video and a Z-projection was used to identify the background of each image. The calculator plus function was used to subtract the background from the image stack so that only moving cells would remain. Using the TrackMate^46,47 plugin in ImageJ,^48,49 cells were identified in each frame and linked together into tracks tracing each cell's movement through the device. This produced approximately 500 tracks per video. Custom python software (https://github.com/nstone8/heimdall) was used to analyze collected cell trajectories. The tracks of live and dead cell populations were analyzed to determine deflection and interaction time with each ridge. The cumulative deflection of the live and dead populations is shown for each of the three flow rates in the supplementary material, Fig. 2. Velocity measurements were taken from TrackMate outputs.

FIG. 2.

Modeling microfluidic device enables balancing of volumetric output to each outlet: (a) the normalized average volumetric output at each outlet for the original tree sorting device design, n = 7. (b) Schematics depicting the two methods for balancing channel resistances for the linear device design: (1) an analytical approach modeling the device as a fluidic circuit and (2) a finite element analysis of the device geometry. (c) The normalized average volumetric output at each outlet for the resistance balanced linear device, n = 11. (d) The normalized average volumetric output at each outlet for the FEA balanced linear device, n = 4. (e) Comparison of the average standard deviation between the normalized volumetric output of outlets 1 to 5 for the three single device designs. (f) The normalized average volumetric output at each outlet for the resistance balanced linear device, n = 12. All error bars depict standard deviation.

Microfluidic flow rate optimization

Cell trajectory videos were collected at three total flow rates—25, 50, and 75 μl/min. All flow rates include a left sheath inlet, cell inlet, and right sheath inlet with a 2.5:1:1.5 ratio, respectively. This sheath flow focused the cells at the entrance of the sorting channel with a bias toward the soft outlet side. A high-speed video was collected at each of the prescribed flow rates and the sorted cells were tracked. The tracked cells were used to plot the cumulative deflection of the live and dead cell populations to determine the difference in the trajectory of the two populations at each of the flow rates.

Sorting evaluation and flow cytometry

Sorting experiments were conducted at the optimized flow rate of 50 μl/min total flow rate. Cells were collected from the five outlets via tubing into conical tubes and stored on ice before analysis with flow cytometry using an Accuri C6 Plus. Using the inlet mixed population and two one-color cell controls, gates on the forward scatter and side scatter plot were set to separate cells from debris as well as the fluorescence gates for green, live cells (FL1) and red, dead cells (FL4). The event count and amount of fluid processed were used to identify cell concentrations and ratios before and after sorting of both the live and dead cell populations. Flow cytometry data was analyzed using FlowJo software.

Enrichment, purity, cell yield, and throughput analysis

Enrichment for live and dead cells, purity, cell yield, and throughput were calculated for each sample using equations 5, 6, 7, 8, and 9, respectively,

$$\begin{array}{rl}& \mathrm{Live}\mathrm{Enrichment}\\ & ={(\text{\%}\mathrm{Green}/\text{\%}\mathrm{Red})}_{\mathrm{Sorted}\mathrm{Outlet}}/{(\text{\%}\mathrm{Green}/\text{\%}\mathrm{Red})}_{\mathrm{Inlet}},\end{array}$$ (5)

$$\begin{array}{rl}& \mathrm{Dead}\mathrm{Enrichment}\\ & ={(\text{\%}\mathrm{Red}/\text{\%}\mathrm{Green})}_{\mathrm{Sorted}\mathrm{Outlet}}/{(\text{\%}\mathrm{Red}/\text{\%}\mathrm{Green})}_{\mathrm{Inlet}},\end{array}$$ (6)

$$\mathrm{Purity}={\left(\frac{\mathrm{Target}\mathrm{Cell}\mathrm{Count}}{\mathrm{Total}\mathrm{Cell}\mathrm{Count}}\right)}_{\mathrm{Sorted}},$$ (7)

$$\mathrm{Cell}\mathrm{Yield}=\frac{\mathrm{Target}\mathrm{Cell}\mathrm{Coun}{\mathrm{t}}_{\mathrm{Sorted}\mathrm{Outlet}}}{\mathrm{Target}\mathrm{Cell}\mathrm{Coun}{\mathrm{t}}_{\mathrm{All}\mathrm{Outlets}}},$$ (8)

$$\mathrm{Throughput}=\mathrm{Inlet}\mathrm{Cell}\mathrm{Concentration}\times \mathrm{Flow}\mathrm{Rate}.$$ (9)

Purity was calculated for live and dead cells for combinations of outlets 1 and 2 and outlets 4 and 5. Cell yield was calculated for live and dead cells for combinations of outlets 1 and 2 and outlets 3, 4, and 5.

RESULTS

Multiplexing a three-inlet and five-outlet platform using a two-layer approach

Inlets and outlets to microfluidic channels frequently feature a symmetric layout to balance the fluidic resistance [see, for example, the “tree” design in Fig. 1(c)]. In our original device design, we ensured that the five outlets were equidistant from the exit of the sorting channel to balance the exit flows of fractionated cells for each mechanical subtype.⁴² For the “tree” device, there is an even distribution of volumetric output to each outlet across multiple experiments, with normalized output ranging from 0.946 to 1.124 [Fig. 2(a) with no statistical difference in output to any of the five outlets using a one-way ANOVA, F > 0.1]. The equidistant outlet approach is appropriate for a single channel but designing a second layer to interface with multiple sets of equally spaced inlets and outlets is more complex and time consuming and the spacing also results in an inefficient use of area for a whole device footprint.

We linearized the inlets and outlets to each channel in a horizontal orientation for three reasons. First, the linear design was more space efficient and allowed a smaller footprint for the multiple channels in comparison to the tree design. Second, aligning all like outlets in the horizontal plane allowed us to use simple, vertical channels to connect the separation layer and the manifold layer with ease. Third, the linear design aligned to a 96-well plate format which allowed simpler testing of the outputs of the individual channels with a multichannel pipettor without the use of the manifold layer. An analytical model was used to calculate channel resistance and balance flow rates through each outlet. With Eq. (3), the width of each channel can be easily calculated by using the channel lengths required by the linear design and a starting channel width. The width of the shortest channel was set to be 100 μm. Using 100 μm as w₂ in Eq. (3), the rest of the equation was filled with design geometries to calculate the width for other channels to match resistance. The initial channel widths were then further optimized using two-dimensional finite element modeling to determine fluid pressure drops and flow rates [Fig. 2(b)]. The final designs generated by both models are described further in the supplementary material (Fig. 3). The resistance balanced linear device and the FEA balanced linear device were validated by measuring the volumetric flow rate at each outlet. The normalized flow rates ranged from 0.869 to 1.063 and 0.917 to 1.068, respectively. In experimental measurements of volumetric flow, we found outlet three of the resistance balanced linear device to have a statistically lower output compared to all other channels, using a Tukey HSD post-hoc test, p < 0.01 [Fig. 2(c)]. For the FEA balanced design, outlet 5 had a statistically lower output compared to outlets 1 and 2, using a Tukey HSD post-hoc test, p < 0.05 [Fig. 2(d)]. Comparing the average standard deviation between normalized volumetric output for each outlet, both the resistance balanced, and FEA balanced linear devices saw reduction in outlet variability compared to the “tree” design [Fig. 2(e)]. The variation in flow rate at each outlet that was observed can be attributed to assumptions for using a 2D FEA approach, inaccuracy in channels and vias as a result of the molding process, and deformation of PDMS under high pressures.⁵⁰ Further iteration of the channel geometries would reduce the small flow rate differences between outlets. Cell separation experiments were carried out using the resistance-balanced designs as they maximized the flow rate to outlet five.

This optimized resistance-balanced linear design was duplicated for eight channels on a wafer to create the high-throughput sorting [in green, Fig. 3(a)]. The manifold layer interfaces and combines the 24 inlet ports and 40 outlet ports to simplify liquid handling, shown in blue, Fig. 3(a). The manifold was bonded on top of the sorting channel to maintain visibility of the sorting channels for microscopy. Resistance modeling was used to create initial designs of the channel geometries and balance the pressure drop from a single inlet to eight channel inlets. The resulting channel widths were input into COMSOL to adjust the manifold channel widths to evenly distribute to each inlet and recombine like outlets with the lowest variation between channels. Figure 3(b) shows the different channel widths used in both layers to balance the flow throughout the equivalent paths.

FIG. 3.

Top manifold layer evenly splits fluid flow to bottom multiplex device layer: (a) the multi-layer multiplex device consists of two layers—a bottom sorting layer (left, green) with 8 parallel sorting devices and a top manifold layer (right, blue) for fluid distribution and recombination. The middle panel shows the alignment of the two layers which are connected by vias where the two layers overlap. The blue circles that do not overlap with the green layer are where the combined inlets and outlets are connected. (b) Detail image shows how differing channel widths are used to balance the fluid flow. (c) High-speed video cell tracking was used to determine the velocity of fluid in each channel of the multiplex device. The data from two replicates are displayed with an average of 100 cells tracked per channel. The error bars depict standard deviation.

The five combined outlets of the eight sorting channels should have equal flow rates to ensure all cell paths through each channel are equivalent. Measuring the volumetric flow rate at each of the five combined outlets, we did see consistent normalized volumetric output to all five outlets with output ranging from 0.897 to 1.055. Outlet three had a statistically lower output compared to all other channels and outlet five had a statistically lower output compared to outlet two [Tukey HSD post-hoc test, p < 0.05, Fig. 2(f)]. Using video tracking, we determined the average velocity of cells in each of the eight channels during operation. A slight variation of flow velocity (mean: 47.0 mm/s, standard error: 15.5%) was observed in all channels with the fastest flow in the middle channels and the slowest flow in the outer channels [Fig. 3(c)]. The variation in velocity corresponds to a volumetric flow rate between 40 and 65 μL/min. Comparing this variation to previously tested flow rates (supplementary material, Fig. 2), this velocity range is acceptable for effective sorting between the viable and non-viable cell populations. Like the linearized channel outlets, these differences can be attributed to a combination of a 2D FEA approach, deviation of dimensions in the fabrication process, and deformation of PDMS under flow.

Multiplexing to improve throughput and processing time and maintain enrichment, purity, and cell yield

Apoptotic and necrotic cells after heat treatment are significantly stiffer than live cells (supplementary material, Fig. 4).⁴² After determining the optimal flow parameters for operation of the single tree device which resulted in maximal deflection of the non-viable population at the highest flow rate (supplementary material, Fig. 2), we observed up to 16-fold enrichment of the live cells in the soft outlets and up to 69-fold enrichment of non-viable cells in the stiff outlets [Fig. 4(a)]. The performance of the single linear device was similar with up to 6-fold enrichment of the live cells and 37-fold enrichment of the non-viable cells in their respective outlets [Fig. 4(a)]. In the multiplex device, we observed up to enrichment of 1.3-fold for live cells in the soft outlets and 58-fold enrichment of dead cells in the stiff outlets [Fig. 4(a)]. This shows high enrichment of dead cells in each configuration and is ideal for further studies into cell stiffening.

FIG. 4.

Sorting enrichment maintained when multiplexing, but throughput and processing time are greatly improved: (a) Sorting enrichment comparison for live and dead cells sorted with both the tree and linear single devices and the multiplex device. Please note the log scale axis. Error bars depict standard deviation, n = 4 for single devices and n = 3 for multiplex device. (b) Comparison of throughput in millions of cells per hour between the single devices and the multiplexed devices. Error bars depict standard deviation. (c) Comparison of the processing time required to process increasing number of cells for different applications between the single device and multiplexed device.

The sorting channel geometry and flow rate was equivalent between these test cases, but differences in live-cell enrichment can be attributed to an overall increased channel resistance and longer path length created by the multiplexed design. The channels operate at a nominal pressure drop of 0.2 bar, which includes the recombination manifold resistance. Channel deformations at this applied pressure will lead to larger ridge gap sizes and changes in the sorting profile.⁵⁰ Further optimization of the gap size in the multiplexed configuration will lead to gains in sorting efficiency for live cells. This is further shown in the purity and yield of the sorting process. Across the single tree, single linear, and multiplex linear designs, highly pure samples of stiffened cells were maintained in the stiff outlets (87%, 93%, and 91% purity of dead cells when combining outlets 4 and 5 for the tree, linear, and multiplex designs respectively) [supplementary material, Fig. 5(a)]. A high yield of live cells was sorted to the soft outlets as expected for all designs [82%, 97%, and 83% of live cells going to outlets 1 and 2 for the tree, linear, and multiplex design, respectively, as shown in supplementary material, Fig. 5(b)]. Non-viable cells were also directed to the soft outlets (41%, 79%, and 66% of dead cells going to outlets 1 and 2 for the tree, linear, and multiplex devices, respectively).

The device performance in terms of sorting efficiency and enrichment was replicated from one channel to eight channels. Modeling and testing of a two-layer manifold approach allowed for the significant scale up of throughput while maintaining the same number of inlet and outlet channels. The processing throughput of a single channel was ∼240 000 cells/h. By introducing the multiple parallel channels to our design, we were able to increase the throughput over 8-fold to process over 5.3 × 10⁶ cells/h in a single multiplex device [Fig. 4(b)]. Because of the inverse relationship between throughput and processing time, this improvement in throughput also results in a time reduction from 8.6 days to 9.4 h to process 5 × 10⁷ cells [Fig. 4(c)].

DISCUSSION AND CONCLUSION

We have shown the ability to combine linearized inlets and outlets to produce highly enriched mechanical subpopulations at a much-reduced processing time. In this study, we developed a method to scale complex microfluidic channels by including a stacked manifold layer for the even distribution and recombination of fluid in each of the inlets and outlets that were linearly aligned. This study shows scaling a microfluidic device to eight parallel channels, increasing the overall throughput of processing by over 8-fold. Two modeling approaches were used in succession to produce equivalent volumetric flow from multiple inlets, through a sorting channel, to multiple outlets. Based on previous work leveraging the relationship of cellular mechanics to cellular phenotype, we can now approach similar applications with higher throughput, enabling further discoveries about cell viability, response to chemotherapy, differentiation state, and malignancy.^4,42,51–55

While the two fluid balancing approaches estimated equal flow rates between channels, there are always differences between modeled and experimental results. Based on the experimental results, we were able to choose the combination of approaches that best achieved viability-based sorting for our application. For example, there are implementations in which it is desirable to collect highly enriched, stiffer, more adhesive, larger, or less viscous cells, such as separating cancer cells from liquid biopsy samples, investigating gene expression of mechanically stiffened cells or identifying more differentiated stem cells.^4,53,54 In these cases, it is important maximize volumetric collection of the outlet containing these rare cells of interest (in the stiff outlets four and five in our device). The design balanced by the analytical resistance model alone offers symmetric flow rates between the soft and stiff outlets compared to the asymmetric distribution in the device design that also incorporated FEA balancing. The second iteration device did have a lower variation in volumetric output to each channel as desired, but for our application, we chose to use the device with higher volumetric flow to outlets four and five. This technique of iterative design could be used to further reduce the variation in flow, and we suggest the use of this combination of analytical and computational modeling for other microfluidic parallelization efforts as well. This process outlines the principles required to scale up more complicated devices. While our approach is to linearize outlets and interface with a manifold layer, some devices might not be able to be linearized. In these cases, the fundamentals of the manifold method apply but might require balancing between more complicated manifold channels and rely more heavily on the FEA model.

The microfluidics field has been able to consistently show potential applications on the lab scale, but there are fundamental difficulties in scaling and developing products for commercialization that keeps most applications confined to the lab.⁵⁶ The throughput increase enabled by our new approach allows us to imagine several use-cases for new applications either in mechanical sorting of cells or in other platforms that need improved throughput to unlock their potential. The increased throughput can be leveraged to either increase the number of cells being processed or drastically reduce the processing time [Fig. 4(e)]. For small cell number applications, the multiplexed platform could be used to reduce processing time including the time cells spend out of their ideal culture environment. Our target application implements the multichannel array to enable large volume testing on the order of 50 × 10⁶ cells for large linked data set generation in genome-scale screens.²⁵ The multiplexing process becomes enabling for this task by reducing the processing time from 8.6 days in a single device to 9.4 h. This same level of improvement can be translated to other applications by applying the linearization, analytical estimation, and FEA validation design workflow laid out here.

SUPPLEMENTARY MATERIAL

See the supplementary material for more details about the design of the manifold channel, the optimization process for cell sorting, comparison of the resistance and FEA models, and comparison of sorting purity and cell yield across different device designs.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

K.M.Y. contributed to the conceptualization of the work, methodology development, experimental validation, formal analysis of data, data curation, writing of the original draft, the review and editing of the draft, visualization of data and funding acquisition. P.S. contributed to the conceptualization of the work, methodology development, software development, formal analysis of data, data curation, writing of the original draft, the review and editing of the draft, and visualization of the data. T.C., K.A., and S.B. all contributed to the formal analysis of data and data visualization. T.S. contributed to the conceptualization of the work, the provision of resources, the funding acquisition, project administration and supervision, and the reviewing and editing of the draft. All authors read and approved the final manuscript. K.M.Y. and P.G.S. contributed equally to this work.

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.