Design and validation of a tunable inertial microfluidic system for the efficient enrichment of circulating tumor cells in blood

Abstract The analysis of circulating tumor cells (CTCs) in blood is a powerful noninvasive alternative to conventional tumor biopsy. Inertial‐based separation is a promising high‐throughput, marker‐free sorting strategy for the enrichment and isolation of CTCs. Here, we present and validate a double spiral microfluidic device that efficiently isolates CTCs with a fine‐tunable cut‐off value of 9 μm and a separation range of 2 μm. We designed the device based on computer simulations that introduce a novel, customized inertial force term, and provide practical fabrication guidelines. We validated the device using calibration beads, which allowed us to refine the simulations and redesign the device. Then we validated the redesigned device using blood samples and a murine model of metastatic breast cancer. Finally, as a proof of principle, we tested the device using peripheral blood from a patient with hepatocellular carcinoma, isolating more than 17 CTCs/ml, with purity/removal values of 96.03% and 99.99% of white blood cell and red blood cells, respectively. These results confirm highly efficient CTC isolation with a stringent cut‐off value and better separation results than the state of the art.

highly efficient CTC isolation with a stringent cut-off value and better separation results than the state of the art. known to be important for critical steps of the metastatic cascade. [4][5][6] Furthermore, CellSearch ® fails to isolate CTCs from tumors in which EpCAM is rarely expressed, such as most squamous carcinomas, sarcomas, lymphomas, melanomas, or neurogenic tumors. 7 Due to the limitations of the methods that, as CellSearch ® , are based on cell surface marker specificity, other methods have been developed that rely on the detection of intrinsic properties of the CTCs. 8 Parsortix ® (ANGLE Biosciences, Toronto, Canada), for instance, enriches CTCs based on their size, by selecting cells able to deform as they traverse through small microchannels. 9 Due to its promising results, ANGLE Biosciences has recently applied for FDA De Novo approval. Other methods, classified under the generic category of inertial sorting methods, take advantage of the balance between viscous, inertial, and secondary flow forces that cells undergo as they travel through microfluidic channels. 10 Some of these methods have recently reached the market. In 2015, the ClearCell ® FX1 System 11 (Biolidics, Singapore) was launched, with the patented microfluidic biochip CTCChip ® FR1. In 2017, Vortex Biosciences (Pleasanton, CA, USA) launched the VTX-1 ® Liquid Biopsy System, a fully automated benchtop system for CTC isolation and collection. 12 Both systems were successfully registered with the FDA as Class I Medical devices and obtained the European conformity (CE) marking for biomedical research. As drawbacks, ClearCell ® FX1 requires blood lysis, thus compromising CTC viability, and both systems work with a fixed, relatively high cut-off detection value of 13 or 14 μm, respectively.
Several inertial-based systems, developed in academic environments, have been proposed to address these limitations. 13 This is the case of the double spiral system, 14 the contraction-expansion array (CEA) microchannel, 15 the spiral channel with periodic expansion structures, 16 or the serpentine-shaped microchannel. 17 Other systems combine different techniques to obtain higher throughput and better performance. 18,19 Among these academic methods, the double spiral system provides a priori superior performance due to improved particle focusing and higher throughput. It was validated by separating 5 μm from 15 μm-sized beads (i.e., 10 μm separation range), and two cancer cell lines (15.7 μm 20 and 19.74 μm 21 average cell sizes) from the remaining blood cell types, using a mixture of those cell lines with non-lysed blood. Interesting as it is, this system lacks critical design and fabrication guidelines, including a design of the outlets that guarantee a balanced hydraulic resistance, required to ensure the appropriate particle trajectories toward their outlets. Furthermore, this system implements a high cut-off separation value that might leave small CTCs undetected, and is yet to be evaluated in real CTC isolation scenarios.
In this article, we describe the design and fabrication of a double spiral inertial system, based on the background of the involved physical properties, computer simulations, and specific predefined separation requirements that improve the state of the art. We compared our computer simulations with experimental results obtained using calibration beads, which led to improved simulations that introduce a novel formulation of the lift coefficient of the inertial lift force term.
This in turn allowed us to produce an improved, redesigned version of the device. Finally, we experimentally tested the CTC isolation capacity of our system in realistic scenarios consisting of cancer cell lines mixed in blood and with a mouse model of metastatic breast cancer, comparing the results obtained with a state-of-the-art method. Then, as a proof of concept, a sample from a patient with hepatocellular carcinoma was processed to detect CTCs.

| Microfluidic chip design
As explained in the Background section (Supplementary Methods S1), the combination of inertial and Dean forces within a properly parametrized spiral-shaped microfluidic channel can be used to separate particles based on their size ( Figure S1). Several spiral designs have been proposed, for example, Fermat, 22 Archimedean, 23 or double Archimedean. 14 These designs use trapezoidal 24 or rectangular 25 channel sections, and some use an extra inlet channel to focus all particles on one side of the channel at the beginning of the spiral. 26 Among those, we chose a design based on a double Archimedean spiral due to its increased length compared to the simple spiral, which helps particle focusing. We aimed at developing a system able to separate particles with a cut-off value of 9 μm, and a 2 μm separation range, that is, able to separate 8 μm from 10 μm particles, as would be required to separate CTCs larger than 9 μm, from erythrocytes and small leukocytes, without a significant loss of CTCs in the process. Besides this general goal, the specific requirements of our system, derived from the theory are: (#1) the system must focus particles into thin streamlines. This requires a minimum channel length (L f ) that depends on the geometry of the channel, the diameter of the particle, and the fluid flow. Moreover, the system must satisfy the experimental value of confinement ratio (CR >0.07). 27 (#2) The ratio between the lift and Dean forces within the channel must be close to 1. Besides these theory-based requirements, an additional functional requirement was established (#3) to minimize the processing time, that is, maximize the flow speed.
Following Sun et al., 14 we opted for a double spiral channel with rectangular section, with 12 concentric loops that switch from counterclockwise to clockwise after the sixth loop ( Figure S2a). Our device's cross-sectional dimensions are 300 μm (width) and 85 μm (theoretical height). The total length of the device channel is 334 mm. The curvature radii (R) for each loop are listed in Figure S2a dimensions render an aspect ratio (AR) of 0.283, which contributes to fulfilling requirement #1. Finally, the ratio between forces ranges from 0.5 for 6 μm particles to 5.5 for particles 20 μm in diameter. For our cut-off value of 9 μm particles, the calculated ratio is 1.12. These ratios are close enough to one (requirement #2) to ensure sorting particles in the desired size range, that is, between 6 and 20 μm.
Special attention was paid to the design of the outlet section to ensure that each particle stream flows undisturbed into the desired outlet channel. A key parameter that affects the particle stream distribution is the resistance of the outlet, which is proportional to the flow, as described by Hagen-Poiseuille's law. 28 A poor definition of the outlet channel resistance may cause a streamline to be directed to a nondesired outlet, decreasing the efficiency of the system. 29 Oh et al. 30  Based on this design, one CAD file was produced ( Figure S2d) from which two silicon wafers were fabricated (Wafers 1 and 2). The system was later redesigned to replace the output trifurcation ( Figure S2b), with a simpler bifurcation, to widen the channel 66.6% (from 300 to 500 μm) before the bifurcation to allow easier particle separation ( Figure S2c

| Optimization of the device: Fabrication protocol and linearity
The small area and long length of the microfluidic channel result in high hydraulic resistance, which in turn produces significant pressure loss within the device. The operating pressure needed to compensate for this loss, estimated at 4 bars for our target operating flow, can deform the PDMS, altering the geometry of the device. Therefore, we optimized the fabrication protocol to produce a rigid enough PDMS that would remain undeformed under this high pressure. For this purpose, inspired by Johnston et al., 31 we compared four PDMS curing protocols (Table 1).
Five microfluidic devices were fabricated from Wafers 1 and 2 following each fabrication protocol. Five milliliters of water were inserted into the devices at increasing pressure values. For each device and pressure point, the average ratio between the experimental and theoretical flow (Q exp /Q th ) was calculated (n = 5), to estimate the PDMS deformation.
The experimental flow Q exp was obtained by measuring the volume extracted from the outlet system during 5 min using the setup described in Supplementary Methods S3. The theoretical flow Q th was calculated from the geometry of the channel, thus assuming a perfectly rigid device. The results ( Figure 1a) show that the protocols that use two temperatures and curation periods (FP2 and FP4) produce the most rigid microfluidic devices, as revealed by their lowest Q exp /Q th ratios. Specifically, the ratios obtained using FP2 and FP4 are similar and remain below 1.05-that is 5% deformation-for working pressure values under 4 bars. Therefore, protocol FP2 was selected as it requires using less curing agent. Next, we calculated the relationship between flow and pressure for the device. that also incorporates the geometry of the device, allowing us to account for the channel height and its effect in the particle trajectories within the channel.
To evaluate these approximations of C l , we compared the simulated and experimental distance between the bead streamlines and the inner wall, just upstream the outlet system. To this end, we used PMMA beads of 6, 8, 10, 12, and 20 μm (Table S1) Figure S4). The average and standard deviation of the distance between each bead streamline and the inner side of the microchannel is shown in Figure 2a.
We then compared the experimental values obtained for WB1 with the simulated ones, for a working flow of 860 μl/min that corresponds to a pressure loss of 2800 mbar (see Figure 1b). Table S2

| Experimental validation of the device
We first quantified the enrichment capacity of our device using These improved results are due to the use of a design that is based on specific requirements, simulated and optimized using a customized lift force coefficient; to the use of a balanced output system; and a PDMS fabrication protocol that guarantees very low channel deformation.

| Mouse model of breast cancer metastasis
The ability of our device to detect and isolate CTCs from blood samples was validated in three steps: (i) first, we evaluated the effect of blood dilution on CTC detection efficiency, obtaining a threshold  Figure 4 shows the total number of CTCs detected by both systems. As seen, our system provides higher detection efficiency (11-fold) compared to Parsortix ® (16,339 vs. 1412 cells/ml detected).
These differences in cell enrichment may be explained by the physical separation principle used by Parsortix ® , which forces cells to deform through a 6.5 μm pore channel. Therefore, the nuclear size becomes the critical feature, which might lead to the detection of only the largest CTCs (Figure 5d). Regarding time performance, our system is 8.5% faster than Parsortix ® for the same volume of processed blood. This difference is magnified considering that, in the same volume of blood, our system detects 11 times more CTCs than Parsortix ® . Altogether, our system provides improved CTCs isolation with smaller sample volume and processing time. The reduced processing time should be in benefit of the cell viability for downstream analysis, and the small volume requirement might be beneficial in longitudinal studies that required multiple blood draws.

| Morphological characterization of the detected CTCs
To characterize the detected CTCs, we measured their size from images taken using a fluorescence Zeiss Cell Observer ® microscope with a 20Â magnification objective and an Endow GFP spectral cube (#1031 346 Zeiss). Figure 5 shows a representative cell from the original 4T1 GFP cell line (Figure 5a), a cell detected with Parsortix ® (Figure 5b), and a cell detected by our inertial system (Figure 5c)

| Proof of concept with human samples
To calculate the purity of our sorted samples, we first measured the capacity of our system to remove the different blood subpopulations, by running blood from five healthy donors through our system. The Cells isolated by our system were labeled with an antibody panel designed to identify CTCs (glyp-3 and asgpr1), as well as the nuclear marker SiR-DNA. Moreover, CD45 antibody was used to discard blood leucocytes (PBLs). Our confocal microscopy-based analysis revealed at least 17 cells/ml, which show a glyp-3 + / asgpr1 À /CD45 À (cell #2 in Figure 6) or glyp-3 + /asgpr1 + /CD45 À (cell #3 in Figure 6) profile. These cells are candidates of being CTCs of hepatic origin. Another subset of cells displays a hybrid behavior (cell #4 in Figure 6), combining hematopoietic and tumor markers.
According to the literature 37 their presence has been associated with disease stage and overall survival.
F I G U R E 6 Cell surface profile isolated by our system. Each column shows a representative field of view of a microscope extension of isolated material. Cell #1 shows a representative cd45 + cell corresponding to the PBL subset. Cells #2 and #3 correspond to CTC candidate cells, which express glyp-3 + /asgpr1 À /cd45 À and glyp-3 + /asgpr1 + / cd45 À markers respectively. Cell #4 suggests a CHC cell profile (glyp-3 + / asgpr1 + /CD45 + ). We have experimentally evaluated the relationship between the fluid velocity, the working pressure point, the cross-section of the device, and the efficiency of the separation using calibration beads.
We also provide an optimized fabrication protocol that ensures rigid enough PDMS for the pressure used. Then we validated the performance of the device using mouse blood artificially mixed with cancer cells, and a mouse model of cancer metastasis to test the performance of our system in a real scenario of CTC detection and enrichment.
Finally, we performed a proof-of-concept experiment using human samples, obtaining an efficiency removing WBC and RBC of 96.03% and 99.99%, respectively, and isolating more than 17 candidate CTCs/ml from a hepatocellular carcinoma patient sample. In summary, in this article, we have presented and validated a double spiral microfluidic chip design that can sort and enrich CTCs from blood (starting at 1:94 dilution) at fluid flows ranged from 800 μl/min to 1.7 ml/min, which can be multiplied using parallel set-ups to compensate for the dilution needed for larger samples, that is, 7 ml of whole blood. Our device displays a cut-off value of 9 μm that can be modified by finetuning the fluid flow or pressure applied to the system. Larger changes in the cut-off value can also be performed using our computer simulations that implement an optimized version of the lift inertial force and incorporates the most relevant elements of the physics of the underlying forces. Table 2 summarizes the main differences between our system and a selection of the systems described in the literature, highlighting some of the advantages of our system. In summary, we believe that we have provided important theoretical, computational, and practical fabrication and experimental insights that prove the potential of inertial sorting as a tool for effective CTC isolation and enrichment. Carlos Ortiz-de-Sol orzano: Conceptualization (equal); funding acquisition (equal); methodology (equal); project administration (equal); resources (equal); writingoriginal draft (equal).

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