Microfluidic deformability-activated sorting of single particles

Mechanical properties have emerged as a significant label-free marker for characterizing deformable particles such as cells. Here, we demonstrated the first single-particle-resolved, cytometry-like deformability-activated sorting in the continuous flow on a microfluidic chip. Compared with existing deformability-based sorting techniques, the microfluidic device presented in this work measures the deformability and immediately sorts the particles one-by-one in real time. It integrates the transit-time-based deformability measurement and active hydrodynamic sorting onto a single chip. We identified the critical factors that affect the sorting dynamics by modeling and experimental approaches. We found that the device throughput is determined by the summation of the sensing, buffering, and sorting time. A total time of ~100 ms is used for analyzing and sorting a single particle, leading to a throughput of 600 particles/min. We synthesized poly(ethylene glycol) diacrylate (PEGDA) hydrogel beads as the deformability model for device validation and performance evaluation. A deformability-activated sorting purity of 88% and an average efficiency of 73% were achieved. We anticipate that the ability to actively measure and sort individual particles one-by-one in a continuous flow would find applications in cell-mechanotyping studies such as correlational studies of the cell mechanical phenotype and molecular mechanism.


Supplementary Text Numerical simulation under the worst-case scenario
A two-dimensional computational domain (Supplementary Figure 1A) was used to explore the effect of the parameters (e.g., sample flow rate, sorting pressure, the spacing between particles, and pressure relaxation time) on the sorting performance. The Navier-Stokes equations (Eq. 1) and particle tracing equations (Eq. 2) were used to model the particle motion in the microfluidic channel network during the hydrodynamic actuation.
where ρf is fluid density, µ is dynamic viscosity, t is time, U is fluid velocity, p is applied pressure, and I is identity tensor. Constant volume flow rate boundary condition was used at the sample inlet. The time-dependent pressure was applied in parallel sorting flows based on the sorting configuration. To include hydrodynamic impedance (resistance and capacitance) in the model, a characteristic time (pressure relaxation time) was added in the time-dependent pressure profile.
The atmospheric pressure is applied as the outlet boundary condition.
The particle motion was explained by the drag force exerted on the particle. The governing equation for particle tracing is as follows: where FD is the drag force, νp is particle velocity, mp is particle mass, ρp is particle density, and dp is particle diameter. The particles were assumed to be a circular shape with a density of 1050 kg/m 3 and diameter of 5 µm.
The particle spacing time Ts is related to the sample concentration as C = 1/ , where W is the width, L is length, and H is the height of the channel (Supplementary Figure 1B). The velocity of the particle Vp is = / , where Ts is time spacing between adjacent particles. Vp can also be expressed in terms of volume flow rate as = ̇/ ( ), where ̇ is the volume flow rate.
Therefore, the particle spacing time Ts can be written as = 1/( ) .
Supplementary Table 1 summarizes all parameters and boundary conditions used in this study.
Supplementary Table   Table S1. Effective sorting parameters used in the numerical simulation.   (1) Generation of agarose beads in mineral oil, (2) Agarose beads after gelation, (3) Agarose beads after washing and dispensed into PBS solution. We found the agarose beads start to coalesce with each other after washing and dispensed into PBS solution. After about 1 hour, these agarose beads were fully dissolved into the PBS at room temperature. This behavior is likely due to our agarose beads were not strongly cross-linked.  Figure S3. Microscope images of in-house fabricated 12.5% PEGDA hydrogel beads. The bead size variation before the filtration comes from the pressure variations in the droplet microfluidic chip. After the filtration, uniform beads with diameters of ~14 µm were obtained. Figure S4. Detailed system diagram for the deformability activated sorting device. The real-time deformability sensing algorithm detects the particle transit time within a rolling sampling window, which is used to trigger a fast-switching solenoid valve for sorting.

Supplementary Video
Supplementary Video 1. (duration: 35 s) Representative cases of successful (example 1) and unsuccessful (example 2 and 3) particle sorting in the numerical simulation.
Supplementary Video 2. (duration: 10 s) Hydrodynamic sorting by order using Polystyrene bead. Sample flow deflection was visualized using fluorescence dye (bright area). The video was recorded with a high-speed CCD camera with the frame rate of 125 fps and played at 30 fps.
Supplementary Video 3. (duration: 4 s) Synthesis of uniformly sized PEDGA hydrogel microbeads using microfluidic droplet generator. The PEDGA hydrogel microbeads were used as model deformability particles. The video was recorded with the frame rate of 30 fps and played at 30 fps.
Supplementary Video 4. (duration: 7 s) Deformability activated sorting of PEGDA hydrogel beads with two deformability population. Beads with brighter edges (fluorescence dye added) were rigid and dark beads were soft. The video was recorded with the frame rate of 30 fps and played at 30 fps.
Supplementary Video 5. (duration: 12 s) Deformability activated particle sorting system user interface in action. The software detects the individual particle transit time online to actively trigger the sorting.