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Recently, technologies have emerged that use hydrodynamic forces to select CTCs based on size and deformability without the use of physical structures. This strategy reduces the risk of device clogging and potentially improves purity. Here, we discuss two examples of such hydrodynamic size selection.

The Vortex technology (Figure 1.9D; Vortex Biosciences, Inc.) is comprised of eight long and narrow microfluidic channels with occasional short segments of side channels that abruptly enlarge the channel width by a factor of ~25. When the sample is infused into the central channel, high volumetric flow rates (~30 mL/h per channel) align cells at an equilibrium position closer to the wall.63 _{This is well-} known as the Segré-Silderberg effect and is in part due to a shear-gradient force (𝐹𝑠) that propels cells away from the channel’s midline, which scales as

where 𝑓𝐿 is a dimensionless lift coefficient; 𝜌 is the fluid’s density; 𝑉𝑚𝑎𝑥 is the fluid’s maximum velocity;

𝑊is the channel’s smallest axial dimension; and 𝑎 is the cell’s diameter. As the cell approaches the wall, a lift force 𝐹𝑊 is generated that pushes the cell back towards the midline and counters 𝐹𝑆:

𝐹𝑊= 𝑓𝐿𝜌𝑉𝑚𝑎𝑥2 𝑎6/𝑊4 (1.4)

After establishing an equilibrium position based on the balance of Eqs. (1.3) and (1.4), the cells reach a side channel where the channel abruptly widens (i.e., channel height is now the smallest dimension). 𝐹𝑠 alone now propels the cell into the trap with a velocity that scales by 𝑎2 after taking into account Stokes fluidic drag force. Hence, larger cells (CTCs) move laterally faster, and since the side channel is relatively short, smaller cells including WBCs are less likely to enter the side channel. Uniquely, at these very high volumetric flow rates, circulating vortices form in the side channels that can effectively trap CTCs if they enter the side channel by 𝐹𝑆,63,206 unless too many CTCs enter and push one another out of the vortex (limit of 500 CTCs per device).63 _{To release the trapped cells, the flow rate can be reduced} significantly (0.75 mL/h per channel), at which point the vortices discontinue and the cells elute off-chip.206

The Vortex technology has improved significantly since its inception. The first report demonstrated a recovery of ~23% of MCF-7 cells spiked into WBCs that were pre-purified by red blood cell lysis. The spike ratio was 1:100 CTC:WBC (1:107 _{is expected in clinical samples), yet even with a ~50-} fold dilution in WBC concentration prior to entering the device, purity was limited to 6.6% (~6,500 leukocytes/mL).206 _{In a more recent study, the central channel’s dimensions were fine-tuned for initial cell} focusing and the side-channels were lengthened for an undisclosed effect. The recovery of MCF-7 cells spiked into 10X diluted whole blood remained low at 8-26% with similar results from lysed blood; variability in the recovery between experiments was reported to be due to culture conditions. Clinical sensitivities of 50% and 88% were achieved for small cohorts of breast and lung cancer patients, respectively (Table 1.1). However, purity rose to a very high 57-95% (0.5-12.7 WBCs/mL). A comparison to Hur, et al.’s results (~6,500 leukocytes/mL)206 _{was unfortunately not drawn in the latest report;}63 _it

would be especially interesting to delve into the fluid dynamics that reduced the WBC background. Notably, the side channels were lengthened by ~50%,63 _{and we would assume that the WBCs (with smaller}

𝐹𝑠 forces) would have more time to migrate laterally and potentially interact with the vortices (reducing purity), which was not observed. We suspect that either the fine tuning of cell alignment or subtle dynamics within the vortices themselves may have improved purity.

Another hydrodynamic size separation technology utilizes Dean Flow Fractionation (Figure 1.9E; Clearbridge BioMedics Pte Ltd.). When fluid is infused around a curved channel at high flow rates (6 mL/h), centrifugal forces push fluid in the center of the channel outward, causing two recirculation profiles to form in the top and bottom of the channel (Dean vortices). To utilize these Dean vortices for size separation, a blood sample (diluted 2-fold) is infused into the device, and blood components are pushed to the outer wall of the spiral channel by a sheathing flow of PBS. The channel then spirals for ~10 cm, which is enough time for the blood cells to make one full recirculation and return to the outer edge of the channel. However, larger cells (CTCs) experience a wall-induced lift force (𝐹𝑊) as they approach the channel’s inner edge, thereby slowing their rotation and causing them to achieved one half of a full recirculation. Thus, at the outlet, CTCs reside on the inner side of the channel, where they are skimmed to a separate outlet than the blood components.

Because random cell-cell interactions likely resulted in the ~1% retention of WBCs, the CTC effluent was fed into a second rendition of the device to achieve ~85% cell line recoveries, 100% sensitivity for 20 lung cancer patients (Table 1.1), and a purity of ~1-10% (~440 ± 320 WBCs/mL). Interestingly, a wide size range of CTCs was isolated, including 10 µm CTCs that hypothetically should not have been recovered by Dean Flow Fractionation, suggesting that either cell deformability115 _{or cell-cell interactions} should be included in the underlying theory. The commercialized technology utilizes red blood cell lysis rather than dilution115 _{and has been designed to be a preparatory tool that simply elutes purified CTCs in}

Clearbridge Biomedics Pte Ltd. has already launched its first CTC processing hub (contracted research organization) in China.