{'fraction_non_alphanumeric': 0.028276652655712647, 'fraction_numerical': 0.01496624633804611, 'mean_word_length': 5.039615384615384, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Dynamic Size-Tracking of Single Cells Using Microfluidics-Integrated Microwave Sensors

Cellular size is one of the most important biophysical indicators of the state of a cell. Cellular size can be used as a sensory signal for determining cellular growth and decay trends and can facilitate the testing of novel drugs on cancerous cells. While size measurements have traditionally been performed using optical microscopy and quantitative phase imaging, there is still ample space for sensors with higher resolution and throughput, as well as lower cost. In this respect, microwave resonators have been suggested for detecting single cells in a labelfree manner; however, little has been done to systematically compare the microwave signal output induced by single cells to the cellular size obtained by optical microscopy. Here and for the first time, we demonstrate that the cellular size measurements conducted by microscopy and a microfluidics-integrated microwave sensor indeed correlate, at the single cell level. We further study in real-time the changes in size of single cells that are dynamically trapped around the sensing region and chemically induced to shrink. The strong correlation between the electronic and optical size results indicates that microwave sensors can be used for detecting and sizing single cells in real time.


INTRODUCTION
Precise measurements of cellular size at high speed have opened up avenues for personalized medicine and the early diagnosis of diseases. 1,2 To measure the cellular size, quantitative phase microscopy 1,3,4 can be used to trap a cell and continuously observe the dynamics of size change. However, for point-of-care applications, a system with a smaller form factor, lower cost and ease of use is needed. This need has driven a significant amount of research efforts for developing sensors capable of sizing single cells. [5][6][7][8][9][10][11][12][13][14][15][16] Among the advances with such microscale sensors include the observation of fast mass fluctuations at the single-cell scale 14 and the measurement of the differential drug response of cancer cells derived from different patients. 15 The focus of the aforementioned sensors has been on mass measurements of single cells, as mass is the most suitable metric for the total accumulated material inside a cell. To detect mass changes, micromechanical structures are used that are directly affected by the total mass of the structure, including any attached analyte. However, the performance of micromechanical sensors in a fluidic environment is hindered by the high viscous dissipation of mechanical motion and diffusion-limited capture rate of analytes. 17 As an effective solution to both problems, resonant sensors based on suspended microfluidic channels have been developed. These sensors, suspended microchannel resonators (SMRs), enclose the fluid inside and are operated under vacuum conditions. Originally developed 5,18,19 and optimized 7,8,[20][21][22] mainly by the Manalis group, SMRs are now pursued by numerous research groups. [23][24][25][26][27][28] However, the need for obtaining a suspended hollow microchannel structure imposes stringent conditions for microfabrication and drives the cost of each sensor.
Remarkably, mass is not the only parameter suitable for determining the total material content inside a cell. As a cell synthesizes proteins and biological polymers, such as cytoskeletal proteins and phospholipids, and maintains a concentration imbalance of different electrolytes in its cytosol with respect to the external medium, the total electrical polarizability of the cell is expected to become markedly different than the electrical polarizability of its external environment. [29][30][31] This contrast in electrical polarizability depends on the total material accumulated inside the cell and exhibits itself as a change in the effective dielectric constant and capacitance with respect to the fluid it displaces. Therefore, an electrical sensor capable of resolving minutiae capacitance changes induced by a single cell can be used for sizing single cells in principle. However, at low electrical frequencies (e.g. smaller than 1 GHz), extraneous effects such as Debye screening and cell membrane polarization dominate the response, and techniques working in this range, such as conventional impedance spectroscopy, do not directly yield cellular size. On the other hand, electrolyte ions cannot follow the electromagnetic field and cease to interfere with the response, when the electromagnetic oscillation frequency is faster than the relaxation rates. Relevant relaxation times 32 in this case are i) the bulk diffusion, ii) diffuse layer charge relaxation and most stringently iii) Debye time scales: in practice, frequencies larger than 1 GHz are sufficient to short out the response of the electrolytes and probe into the cellular structure. At these frequencies, hydrogen bonds in the water can still follow the electrical oscillations up to approximately 20 GHz. 33 As a result, a large contrast difference emerges between the extracellular medium (mainly composed of water) and intracellular biostructures (such as cytoskeleton, nucleus and organelles) at the lower end of the microwave frequencies (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) GHz). This contrast difference enables microwave sensors with much larger dimensions to be used to measure cells compared to mechanical sensors. [34][35][36][37][38][39] However, the question remains whether the microwave signal induced by a passing cell indeed correlates with the geometrical size of the cell. By using simultaneous microscopy measurements, we verify that this is indeed the case. We then proceed to use these sensors for sizing single cells in realtime. Our results demonstrate the emerging potential of microfluidics-integrated microwave sensors (MIMS) for single-cell biophysical measurements.

RESONANT SENSOR
To utilize the high sensitivity of microwave frequencies, a coplanar waveguide (CPW) resonator on a fused silica chip was designed to match the 50 Ω impedance of the electronic measurement system (Figure 1a). The CPW narrows down into a bowtie-shaped sensing region that coincides with a microfluidic channel. The on-chip CPW has a signal path of a 3.4 cm length and a 1.6 cm width. The gap between the ground and signal line is 400 µm, which narrows down to 50 µm at the sensing region (Figures S1). In the sensing region where the inter-electrode distance shrinks, the local electric field intensifies to enhance the sensitivity of the detection (Figures S2). As cells pass through the sensing region one by one, they induce distinct frequency shifts in the microwave sensor while being imaged using optical microscopy ( Figure 1b).

EXPERIMENTAL SETUP
In our experimental setup, there were three subsystems: an optical microscope, a microfluidics-integrated microwave sensor, and a fluidic control system that transfers cells to the sensing region ( Figure S3). Initial measurements to find the resonance frequency and the quality factor of the sensor were determined using a vector network analyzer ( Figure S4). To increase the sensitivity of the microwave sensor, we employed a narrow-band detection scheme that is centered around the first resonance frequency of the CPW structure. 40 Phasesensitive detection was performed with a lock-in amplifier and due to the frequency limitation of the lock-in amplifier, we constructed an external heterodyne circuitry 34,35 to continuously track the resonance frequency ( Figure S5). With the PLL, the phase of the resonator was locked to 0 degrees with a proportional-integral (PI) controller. Any deviation from 0 degrees emerges as an error signal updating the frequency of the signal generator. With this method, we can continuously track the resonance shifts. Using the bright field images of the cells, the number of pixels for each single cell was estimated digitally using built-in functions on MATLAB. The size of a pixel was estimated by calibrating the number of pixels with device dimensions. The mean and standard deviation of the size of each cell was obtained by measuring the same cell on many successive frames. The pixelated area was then converted first into the actual area, and then assuming a spherical shape, into the cell volume.
By matching the calculated volume of the cell from microscopy images and the induced microwave frequency shifts, we observed an almost linear relationship ( Figure 2a). Indeed, for cells that passed through the middle of the channel and hence did not overlap with the sensing electrodes (red data points in Figure 2a), the fitting to the linear trend was much stronger than the trend seen in cells whose trajectory overlaps the sensing electrodes (blue data points in Figure 2a). The RMSE (root-mean-square error) values are 0.10 kHz and 0.44 kHz for the non-overlapping and overlapping cells, respectively, and the overall RMSE value is 0.26 kHz. We note that all cells larger than a specific size in Figure 2a  The measurement bandwidth of our system was set to 2 Hz to strike a balance between the Signal-to-Noise ratio and throughput. As a result, a small number of cells which passed through the sensing region faster than 500 ms did not produce full response. These cells were excluded from the analysis since the data from both the microwave sensor and the optical microscopy image were not reliable. On average, the responsivity of the sensor in Figure 2a turns out to be 0.33 / / . With an Allan deviation of 1.8 × 10 '( and resonance frequency of 2.19 GHz, the minimum resolvable frequency is ~ 60 Hz, which results in a minimum resolvable change in volume of 182 / . This level translates into a minimum detectable change in the cell radius of ~145 nm, for a mean cell having radius of 10 . We have also investigated the effect of channel height on frequency shifts. To observe this effect, we fabricated another device with a channel height of 55 µm (which was 110 µm in previous device). We repeated the same experimental and data analysis procedure to obtain the relation between volume and frequency shifts (Figure 2c). Similar to Figure 2a Figure 3a where the sensing region is partitioned into eleven different subsections -along the most densely visited trajectories of the particle flow for each experiment. In Figure 3a, the blue data points indicate a vertical transition path along the sensing electrodes, the red data points are for particles passing in between two electrodes without any overlap, and the green data points indicated the cases where a fraction of the particles overlaps with the top of the signal or ground electrode.
The shift in the resonance frequency turns out to have a local maxima near the edge of each electrode, in line with earlier observations. 41 The frequency responsivity varies by more than half over the signal electrode. The trend in Figure 3a was further investigated by a similar device as detailed in Figure S7. Remarkably, the responsivity at the center of the sensor, where there is no overlap with the electrodes, is constant within the noise level (Figure 3a).
This result indicates that microwave measurements can be used for size measurements, without the need for additional microscopy for position determination, as long as the particle flow is confined within the central region (which can be accomplished by e.g., hydrodynamic focusing, modifying the device design, or introducing position measurement capabilities 40,42 ).   Comparison of the size distributions obtained from frequency shift measurements and through fluorescence microscopy. The histograms for volume and frequency shifts are also projected to their respective axes and in both cases a distinct peak appears as expected The size of the trapped cell was estimated by an image processing algorithm and compared with the frequency shift statistics. We expect the algorithm to yield similar volume values as the same cell was processed in different frames. In fact, Figure 4c illustrates the volume concentrated to approximately 1.18 × 10 ? / with a standard deviation normalized to the mean value ( 2 @ ) of 0.17, which can be seen at the bottom histogram as well in Figure 4c.
Remarkably, the microwave sensor results indicate a relatively narrower distribution for the size of the cell.

MEASURING CHANGES TO CELL SIZE IN REAL TIME
The ability to dynamically monitor the effects of a drug delivered to diseased cells is of utmost importance. One such dynamical effect of certain drugs is the shrinkage of a cell, which can be detected by MIMS. To this end, after we have shown that single cells can be trapped and their frequency shift statistics measured, we designed another experiment to detect the biophysical change in a single cell. We tracked the resonance frequency of a MIMS device (at approximately 2.72 GHz) with frequency stability of 1 × 10 '( . To demonstrate that microwave sensors can track the real-time dynamics of individual cells, we chose to use dimethyl sulfoxide (DMSO), a chemical that accelerates dehydration, 43 to induce a dynamical change in the size of the cell. We observed that the effect of DMSO is optimal when treating the cells for approximately half an hour in their culture plate. For the experiment, cells were pretreated for 15 minutes to capture the initial dynamics of cell shrinkage. After the pretreatment, the cells were transferred to the microchannel, and a target cell among the population was selected and trapped around the sensing region. Then, the applied pressure was directed in either direction continuously and the electronic data were recorded ( Figure 5). As DMSO causes a contraction of the interfacial region between water-lipid boundary 44 , we expected to see a shrinkage in the lipid bilayer of the cells causing smaller sizes. In Figure 5a, the ten-point moving average of the shifts decreased from 6.43 kHz to 4.64 kHz (Figure 5a) within thirty minutes. For the control run, another cell population was processed in the same way, replacing DMSO with cell culture. Using the same device, another cell from the control cell population was tracked for more than twenty minutes. Throughout the experiment, the average frequency shift remained close to the original signal level (5.46 kHz to 5.11 kHz).
Analytically, we estimated the amount of shift that is caused by the cell in between the electrodes (Supplementary Note 1). In the calculations, we have utilized the permittivity contrast between the cells and fluid that modulates the capacitance of the overall system.
Using the dimensions and resonance frequency of the fabricated devices, the change in the resonance turns out to be approximately a few kHz and in accordance with the experimental results as in Figure 2a. Usually, the relative changes in the cellular size as a function of control parameters (e.g., introduced drugs) are more relevant than the absolute size determination. To accurately determine the cellular size from a given sensor, a calibration procedure using analytes of known size and permittivity values can be conducted first (similar to the microparticle measurements of Figure 3). By utilizing MIMS technology, the drug sensitivity of diseased cells (e.g. cancerous cells) to various remedies can be predicted with lower cost and reliable sensitivity.

DATA AVAILABILITY
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

CODE AVAILABILITY
The computer codes generated during the current study are available from the corresponding author on reasonable request.