I. INTRODUCTION

Section:

ChooseTop of pageABSTRACTI. INTRODUCTION <<II. MATERIALS AND METHODSIII. RESULTS AND DISCUSSI...IV. CONCLUSIONSREFERENCESUp to date, the most sophisticated laboratory equipment ensuring a complete analysis of particles in suspension is a Flow Cytometer.11. A. Cossarizza, H. D. Chang, A. Radbruch, M. Akdis, I. Andrä, F. Annunziato, P. Bacher, V. Barnaba, L. Battistini, W. M. Bauer, and S. Baumgart, “Guidelines for the use of flow cytometry and cell sorting in immunological studies,” Eur. J. Immunol. 47(10), 1584–1797 (2017). https://doi.org/10.1002/eji.201646632 It is routinely used in diagnostic and research fields to detect physical and chemical features of cells22. H. Cong, F. C. Loo, J. Chen, Y. Wang, S. K. Kong, and H. P. Ho, “Target trapping and in situ single-cell genetic marker detection with a focused optical beam,” Biosens. Bioelectron. 133, 236–242 (2019). https://doi.org/10.1016/j.bios.2019.02.009 and to count them.In this paper, the combination of two algorithms, a cell counting algorithm and a velocity algorithm based on a Digital Particle Image Velocimetry (DPIV) method, is presented to investigate the collective behavior of particles, in micro-channels or chambers, in response to hydrodynamic stimuli. The proposed data analysis procedure offers the advantage to extract automatically the information on the number of particles, flowing in an investigated area in time, and their velocities. A set of experiments were carried out to validate the method proposed in this paper and the results obtained show a significant variation in the hydrodynamic responses to external stimuli and the possibility to associate them with the particles’ physical properties. The simplified optical setup and the algorithm flexibility, make this methodology suitable for real-time detection in embedded systems for the study of cell interaction, as in the Lab-on-a-Chip. A microfluidic-based system able to detect variations in number, concentration, and shape of particles as well as their hydrodynamic properties would considerably improve the identification of various physiological and pathological conditions. The consistency of a biological fluid may change depending on the intrinsic properties of the particles and fluids used, or alterations induced by a disease of the organisms examined may occur. The blood is an example, which is composed of cells with distinguishable traits like size, shape, surface characteristics, compactness, and plasma composition.33. P. K. Dagur and J. P. McCoy, Jr., “Collection, storage, and preparation of human blood cells,” Curr. Protoc. Cytom. 73(1), 5.1.1–5.1.16 (2015). https://doi.org/10.1002/0471142956.cy0501s73 All these listed items affect the differentiated migration dynamics of specific blood particles/cells. Some pathological diseases, such as atherosclerosis or thrombosis, can be associated directly with blood disorders altering the cells’ movement, whereas others, like anemia or leukemia, affect the cells’ proliferation and indirectly the flow.44. S. Losserand, G. Coupier, and T. Podgorski, “Migration velocity of red blood cells in microchannels,” Microvasc. Res. 124, 30–36 (2019). https://doi.org/10.1016/j.mvr.2019.02.003,55. A. Arboix, C. Jiménez, J. Massons, O. Parra, and C. Besses, “Hematological disorders: A commonly unrecognized cause of acute stroke,” Exp. Rev. Hematol. 9(9), 891–901 (2016). https://doi.org/10.1080/17474086.2016.1208555For over a century, manual cell counting with the use of a cytometer and a microscope has been the prevalent technique in laboratories, despite requiring bulky equipment and being a time-consuming approach. As an alternative to manual counting, automated cell counters based on the Coulter Counter principle have been developed and become commercially available.66. A. Vembadi, A. Menachery, and M. A. Qasaimeh, “Cell cytometry: Review and perspective on biotechnological advances,” Front. Bioeng. Biotechnol. 7, 147 (2019). https://doi.org/10.3389/fbioe.2019.00147 The limits in their use are to require bulky and costly equipment and a large number of samples and reagents. Advances in microfluidics have shown promising results in the development of low-cost and portable Lab-on-a-Chip devices with higher throughput, sensitivity, and accuracy.7–97. S. Gupta, K. Ramesh, S. Ahmed, and V. Kakkar, “Lab-on-chip technology: A review on design trends and future scope in biomedical applications,” Int. J. Bio-Sci. Bio-Technol. 8(5), 311–322 (2016). https://doi.org/10.14257/ijbsbt.2016.8.5.288. A. M. Streets and Y. Huang, “Chip in a lab: Microfluidics for next generation life science research,” Biomicrofluidics 7(1), 011302 (2013). https://doi.org/10.1063/1.47897519. D. Mark, S. Haeberle, G. Roth, F. Von Stetten, and R. Zengerle, “Microfluidic labon-a-chip platforms: requirements, characteristics and applications,” Chem. Soc. Rev. 39, 1153–1182 (2010). https://doi.org/10.1039/B820557B In the miniaturization efforts, different technological issues have arisen in relation to the biological or chemical application contexts10–1310. M. Salve, K. Amreen, P. K. Pattnaik, and S. Goel, “Integrated microfluidic device with carbon-thread microelectrodes for electrochemical DNA elemental analysis,” IEEE Trans. Nanobiosci. 21, 322–329 (2021). https://doi.org/10.1109/TNB.2021.312165911. H. Y. Tan and Y. C. Toh, “What can microfluidics do for human microbiome research?,” Biomicrofluidics 14(5), 051303 (2020). https://doi.org/10.1063/5.001218512. D. B. Weibel and G. M. Whitesides, “Applications of microfluidics in chemical biology,” Curr. Opin. Chem. Biol. 10(6), 584–591 (2006). https://doi.org/10.1016/j.cbpa.2006.10.01613. D. Janasek, J. Franzke, and A. Manz, “Scaling and the design of miniaturized chemical-analysis systems,” Nature 442(7101), 374–380 (2006). https://doi.org/10.1038/nature05059 and to the detection approaches.14–1714. G. Ochoa-Vazquez, B. Kharisov, A. Arizmendi-Morquecho, A. Cario, C. Aymonier, S. Marre, and I. López, “Microfluidics and surface-enhanced Raman spectroscopy: A perfect match for new analytical tools,” IEEE Trans. Nanobiosci. 18(4), 558–566 (2019). https://doi.org/10.1109/TNB.2019.294307815. G. Aubry and H. Lu, “A perspective on optical developments in microfluidic platforms for Caenorhabditis elegans research,” Biomicrofluidics 8(1), 011301 (2014). https://doi.org/10.1063/1.486516716. L. Novak, P. Neuzil, J. Pipper, Y. Zhang, and S. Lee, “An integrated fluorescence detection system for lab-on-a-chip applications,” Lab Chip 7(1), 27–29 (2007). https://doi.org/10.1039/B611745G17. I. Grabowska, M. Sajnoga, M. Juchniewicz, M. Chudy, A. Dybko, and Z. Brzozka, “Microfluidic system with electrochemical and optical detection,” Microelectron. Eng. 84(5–8), 1741–1743 (2007). https://doi.org/10.1016/j.mee.2007.01.248 It is significant to mention the recent advancement in the use of microfluidics for the study of physiological processes as in the case of organs-on-chip,1818. N. Azizipour, R. Avazpour, D. H. Rosenzweig, M. Sawan M, and A. Ajji, “Evolution of biochip technology: A review from lab-on-a-chip to organ-on-a-chip,” Micromachines 11(6), 599 (2020). https://doi.org/10.3390/mi11060599,1919. K. D. Seo, B. K. Kwak, S. Sanchez, and D. S. Kim, “Microfluidic-assisted fabrication of flexible and location traceable organo-motor,” IEEE Trans. Nanobiosci. 14(3), 298–304 (2015). https://doi.org/10.1109/TNB.2015.2402651 and in biology as for the cellular analysis2020. P. Chen, S. Li, Y. Guo, X. Zeng, and B. F. Liu, “A review on microfluidics manipulation of the extracellular chemical microenvironment and its emerging application to cell analysis,” Anal. Chim. Acta 1125, 94–113 (2020). https://doi.org/10.1016/j.aca.2020.05.065,2121. J. Sibbitts, K. A. Sellens, S. Jia, S. A. Klasner, and C. T. Culbertson, “Cellular analysis using microfluidics,” Anal. Chem. 90(1), 65–85 (2017). https://doi.org/10.1021/acs.analchem.7b04519 and cell-to-cell interactions.2222. M. Rothbauer, H. Zirath, and P. Ertl, “Recent advances in microfluidic technologies for cell-to-cell interaction studies,” Lab Chip 18(2), 249–270 (2018). https://doi.org/10.1039/C7LC00815E

This work aims to develop an approach for the investigation of micro-particles moving in micro-channels or chambers suitable for Lab-on-a-Chip implementation. To do that, a wide experimental campaign was carried out, using micro-particles of different natures, as living cells and silica beads, and with different physical properties, such as density and size (from 5 to 16μm). An external oscillating flow was imposed at the inlet of a micro-channel and the process was continuously monitored in a test area simultaneously by using a CCD camera and a photo-detector. The videos and the signals acquired were analyzed to determine information correlated to the changes in time of the micro-particles number and their velocities.

The application of flow visualization in biological systems is becoming increasingly common in studies ranging from intracellular transport to the movements of whole organisms. In cell biology, the standard method for measuring cell-scale flows and/or displacements has been Digital micro Particle Image Velocimetry (micro DPIV).23–2523. A. G. Koutsiaris, D. S. Mathioulakis, and S. Tsangaris, “Microscope PIV for velocity-field measurement of particle suspensions flowing inside glass capillaries,” Meas. Sci. Technol. 10(11), 1037 (1999). https://doi.org/10.1088/0957-0233/10/11/31124. C. D. Meinhart, S. T. Wereley, and J. G. Santiago, “PIV measurements of a microchannel flow,” Exp. Fluids 27(5), 414–419 (1999). https://doi.org/10.1007/s00348005036625. A. G. Koutsiaris, “Digital micro PIV ( μPIV) and velocity profiles in vitro and in vivo,” in The Particle Image Velocimetry—Characteristics, Limits and Possible Applications (Intech Open, 2012). https://doi.org/10.5772/36724 More and more researchers are recently looking to live-cell imaging to provide a quantitative understanding of cellular mechanisms. In Ref. 2626. S. Pradeep and T. A. Zangle, “Quantitative phase velocimetry measures bulk intracellular transport of cell mass during the cell cycle,” Sci. Rep. 12(1), 1–14 (2022). https://doi.org/10.1038/s41598-022-10000-w, a quantitative phase velocimetry (QPV) approach, which uses the principle of PIV, was developed to track the velocity flow of material within a single cell, and in Ref. 2727. T. N. Kim, P. W. Goodwill, Y. Chen, S. M. Conolly, C. B. Schaffer, D. Liepmann, and R. A. Wang, “Line-scanning particle image velocimetry: An optical approach for quantifying a wide range of blood flow speeds in live animals,” PLoS One 7(6), 1–13 (2012). https://doi.org/10.1371/journal.pone.0038590, a live scanning particle-imaging velocimetry (LS-PIV) was implemented to quantify the blood velocity in live mice suffering from a cerebral arteriovenous malformation. They detect the blood velocities and exaggerated pulsatility along the abnormal vascular network in these animals. In Ref. 2828. M. Pereyra, A. Drusko, F. Krämer, F. Strobl, E. H. Stelzer, and F. Matthäus, “QuickPIV: Efficient 3D particle image velocimetry software applied to quantifying cellular migration during embryogenesis,” BMC Bioinformatics 22(1), 1–20 (2021). https://doi.org/10.1186/s12859-021-04474-0, a free and open-source solution for performing efficient and robust quantification of collective cellular migration in the increasingly popular 3D dynamic data sets in life sciences are developed. In Ref. 2929. M. F. Sampedro, G. L. Miño, C. D. Galetto, and V. Sigot, “Spatio-temporal analysis of collective migration in vivo by particle image velocimetry,” Phys. Biol. 18(6), 066008 (2021). https://doi.org/10.1088/1478-3975/ac2e71, the PIV approach was used for analyzing the dynamics of in vivo models of collective migration. That evidences the relevance of the topics and the challenging open issues around them and the effort in finding a straightforward methodology for velocity cell detection.In this work, the micro-particle velocities were computed by taking into account the DPIV method based on image analysis, and the micro-particles number was obtained by a custom counting algorithm. The DPIV methodology was initially used by the authors to study the collective behaviors of RBCs in a micro-channel in unsteady conditions.3030. F. Cairone, D. Ortiz, P. J. Cabrales, M. Intaglietta M, and M. Bucolo, “Emergent behaviors in RBCs flows in micro-channels using digital particle image velocimetry,” Microvasc. Res. 116, 77–86 (2018). https://doi.org/10.1016/j.mvr.2017.09.003,3131. F. Cairone, D. Mirabella, P. J. Cabrales, M. Intaglietta, and M. Bucolo, “Quantitative analysis of spatial irregularities in RBCs flows,” Chaos, Solitons Fractals 115, 349–355 (2018). https://doi.org/10.1016/j.chaos.2018.07.012 Starting from that, in this paper, a further development of this approach is presented to extract automatically the information on the number of particles, flowing in an investigated area in time, and to detect their velocities. Working in the MATLAB environment, it was possible to easily integrate the counting algorithm with the DPIV-based algorithm, to automatically run the analysis to different videos, and to post-process the results in time and frequency domain, showing the suitability for automatic classification of micro-particles in biological fluids. In the considered experiments, it was possible not only to detect the hydrodynamic behavior of the micro-particles, but also to correlate this to their physical features, such as the size and the density of micro-particles.In the last few decades, image processing-based methods32–3532. S. Sunardi, A. Yudhana, and S. Saifullah, “Identity analysis of egg based on digital and thermal imaging: Image processing and counting object concept,” Int. J. Electr. Comput. Eng. 7(1), 200 (2017). https://doi.org/10.11591/ijece.v7i1.pp200-20833. T. Liu, W. Wu, Chen,C. Sun, X. Zhu, and W. Guo, “Automated image-processing for counting seedlings in a wheat field,” Precis. Agric. 17(4), 392–406 (2016). https://doi.org/10.1007/s11119-015-9425-634. N. Ab Azar, A. Babakhani, A. Broumandnia, and K. Sepanloo, “A novel method for detecting and counting overlapping tracks in SSNTD by image processing techniques,” Radiat. Meas. 91, 36–43 (2016). https://doi.org/10.1016/j.radmeas.2016.04.00935. Y. H. Toh, T. M. Ng, and B. K. Liew, “Automated fish counting using image processing,” in International Conference on Computational Intelligence and Software Engineering (IEEE, 2009), pp. 1–5. https://doi.org/10.1109/CISE.2009.5365104 and microfluidics-based systems for particle counting and detection have been developed to overcome the barriers associated with conventional methods,3636. H. Zhang, C. H. Chon, X. Pan, and D. Li, “Methods for counting particles in microfluidic applications,” Microfluid. Nanofluid. 7(6), 739–749 (2009). https://doi.org/10.1007/s10404-009-0493-7,3737. D. Huh, W. Gu, Y. Kamotani, J. B. Grotberg, and S. Takayama, “Microfluidics for flow cytometric analysis of cells and particles,” Physiol. Meas. 26(3), R73 (2005). https://doi.org/10.1088/0967-3334/26/3/R02 but the use of real-time image processing is still very challenging3838. T. Hou, H. Chang, H. Jiang, P. Wang, N. Li, Y. Song, and D. Li, “Smartphone based microfluidic lab-on-chip device for real-time detection, counting and sizing of living algae,” Measurement 187, 110304 (2022). https://doi.org/10.1016/j.measurement.2021.110304 due to hardware and software requirements. In order to overcome these issues for the development of a real-time approach, in this work, the possibility to detect the flows by the use of photo-detector signals as an alternative to camera acquisition has also been investigated. The optical detection by signals was proved to be useful for characterizing the flow non-linearity,3939. F. Schembri and M. Bucolo, “Periodic input flows tuning nonlinear twophase dynamics in a snake microchannel,” Microfluid. Nanofluid. 11, 189–197 (2011). https://doi.org/10.1007/s10404-011-0786-5,4040. F. Schembri, F. Sapuppo, and M. Bucolo, “Experimental identification of nonlinear dynamics in microfluidic bubbles flow,” Nonlinear Dyn. 67, 2807–2819 (2012). https://doi.org/10.1007/s11071-011-0190-4 it was possible for the development of a real-time velocity detection system for the slug flow analysis in a micro-channel4141. S. Gagliano, G. Stella, and M. Bucolo, “Real-time detection of slug velocity in microchannels,” Micromachines 11(3), 241 (2020). https://doi.org/10.3390/mi11030241 and the realization of a micro-optofluidic flow detector for the investigation of biological and chemical samples on chip.4242. F. Cairone, S. Davi, G. Stella, F. Guarino, G. Recca, G. Cicala, and M. Bucolo, “3D-printed micro-optofluidic device for chemical fluids and cells detection,” Biomed. Microdevices 22, 37 (2020). https://doi.org/10.1007/s10544-020-00487-3In this paper, the signals, collected by the photo-detector, were compared with the velocity trends obtained by the DPIV-based algorithm as a proof of concept for a further simplification and speed-up of the data acquisition and analysis, based on a simpler optical detection than the video recording needed for the on-chip implementation. The paper is organized as follows: Sec. describes in detail the experimental setup, the campaign carried out and illustrates the procedures implemented to count the micro-particles and calculate their velocity. Section presents the results obtained from the counting of the micro-particles, the trends obtained from the DPIV-based algorithm and their correlation, the comparison between the velocity trends obtained from the DPIV-based algorithm and the signals obtained from the photo-detectors, and finally the hydrodynamic responses of the micro-particles in the time and frequency domains under different experimental conditions, discussing their correlation with the properties of the micro-particles.

II. MATERIALS AND METHODS

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. MATERIALS AND METHODS <<III. RESULTS AND DISCUSSI...IV. CONCLUSIONSREFERENCES

A. Experimental setup

The experimental setup is composed of a syringe pump, a microfluidic chip, and an opto-mechanical system. The syringe pump (neMESYS low-pressure module, Cetoni GmbH, Korbussen, Germany) was used to inject a fluid mixed with micro-particles in a Y-junction squared rectilinear micro-channel in cyclo-olefin copolymer (SMS0104, Thinxxs, Zweibrücken, Germany), with a length of 16mm and a square cross section with a side of 320μm. Its geometry is shown in Fig. 1(a). The microfluidic process was analyzed in an investigated area at a distance of 8mm from the inlet, illuminated by a white light. A photo-detector, labeled PH (SM05PD1A, Thorlabs, Newton, NJ, USA), with an operating wavelength of 350–1100 nm, connected to an acquisition board (BNC-2110, National Instruments, Austin, TX, USA) and a CCD camera (DCU224, Thorlabs, Newton, NJ, USA), with a resolution of 1280×1024 pixels (pixel size of 4.65μm, square), included both in the opto-mechanical system (Thorlabs, Newton, NJ, USA) allow a simultaneous process monitoring. A magnification of 10x (PLN, Olympus, Tokyo, Japan), with a numerical aperture (NA) of 0.25, a working distance of 10.6 mm, and a depth of focus of 440μm has been used. A distance of 3.5mm between the focal plane and the objective has been considered and due to the geometry of the micro-channel being square-sectioned, there is no loss of visual field, as is usual the case with cylindrical micro-channels.4343. A. G. Koutsiaris, “Loss of field of view due to optical mismatch at the inner diametric plane of cylindrical artificial microvessels,” Results Opt. 8, 100241 (2022). https://doi.org/10.1016/j.rio.2022.100241 A PC with Intel® Core™ i7-6500U CPU @ 2.50 GHz 2.59 GHz, RAM 8 Gb and operative system 64 bit was used for the analysis.The data were recorded for about 75 s, with a video frame rate of 60 frames per second, around 4.500 frames per experiment, and a sampling frequency of 1kHz for the photo-detector acquisition. A detailed description of the opto-mechanical setup is reported in Ref. 4444. F. Cairone, S. Gagliano, and M. Bucolo, “Experimental study on the slug flow in a serpentine microchannel,” Exp. Therm. Fluid Sci. 76, 34–44 (2016). https://doi.org/10.1016/j.expthermflusci.2016.02.011. A flow chart and some pictures of the experimental setup are shown in Figs. 1(b) and 2(a). In particular, Figs. 2(b) and 2(c) show a zoom of the micro-channel together with the objective lens and a zoom of the photo-detector position with an image of the photo-detector used. In Fig. 3, a scheme showing the CCD resolution, the photo-detector resolution, and the region of interest (ROI) selected in the performed experiments and analyzed is shown.

B. Experimental campaigns

The microfluidic chip was fed by an oscillating flow. The biological fluids employed for the experiments were obtained by diluting some micro-particles in a saline solution, the phosphate buffered saline (PBS, a density of 1072 kg/m3). The micro-particles diluted with the PBS were of two types: live cells and artificial beads. The live cells, of eukaryotic origins, were the yeast cells of Saccharomyces cerevisiae and the human epithelial HeLa cells. The relevant difference between these two types of cells concerns their dimension: the yeast cells have a diameter of 5μm while the human cells have a diameter of 16μm. The artificial beads were silica beads with a diameter of 6μm. The number concentration of particles, diluted in 10ml of PBS fluid, was 1×105 for the silica beads, 1×107 for human cells, and 1×108 for the yeast cells. The physical properties of the particles, such as mass, radius, volume, and density, are summarized in Table I.

TABLE I. The physical properties of the micro-particles.

Micro-particlesMass (kg)Radius (m)Volume (m3)Density (kgm3)Yeast cells7.37 × 10−142.5 × 10−66.54 × 10−171126Human cells2.23 × 10−128.0 × 10−62.14 × 10−151040Silica beads1.36 × 10−133.0 × 10−61.13 × 10−161200Initially, a single-phase PBS flow, in the absence of micro-particles, was recorded to quantify the effect of the fluid background in the images and the signals. The PBS flow was injected at the inlet with an oscillating flow at a frequency of fi=0.1Hz and an amplitude of A=0.1ml/min. The following 22 experiments conducted are summarized per type of cells in Table II. The micro-particles flow was fed into the micro-channel using an oscillating flow at a frequency of fi∈Hz and an amplitude strength varying in the range A∈ml/min. For the three categories of particles, five equal experimental conditions were considered with fi=0.1Hz and A∈ml/min. Then, for the yeast cells, the campaign was extended considering three other experiments with fi=0.1Hz and A∈ml/min and four experiments with fi=0.2Hz and A∈ml/min.

TABLE II. The experimental campaigns.

Micro-particlesFrequency fi (Hz)Amplitude A (ml/min)Yeast cells0.10, 0.03, 0.04, 0.05, 0.07, 0.1, 0.15, 0.20.20.05, 0.07, 0.1, 0.2Human cells0.10.04, 0.05, 0.07, 0.1, 0.15Silica beads0.10.04, 0.05, 0.07, 0.1, 0.15

C. Micro-particle counting algorithm

In diagnostic and research life science laboratories, cell counting is a common task for any cell-based assay. The less expensive procedure is to count the cells using a reusable hemocytometer by visualizing them with a bright field optical microscope.4545. M. R. Green and J. Sambrook, “Estimation of cell number by hemocytometry counting,” Cold Spring Harb. Protoc. 11, 732–734 (2019). https://doi.org/10.1016/j.tox.2021.153083 To reduce the systematic and random error of the manually count and to improve the statistic values, these approaches have been automated with micro-particles imaging analysis acquisition based on enhanced technologies and paired with a sophisticated micro-particles counting algorithm.

The proposed procedure provides a continuous counting in time of the micro-particles number in the investigated area, avoiding any manual and individual selecting of the frames to be studied. It analyzes automatically the video, frame by frame, counts the number of particles per frame, and collects this information in a signal.

The micro-particles counting algorithm was implemented in the MATLAB environment and the fundamental steps implemented are listed in the flow chart in Fig. 4. The images, to be analyzed, are loaded automatically in the platform and the first step is the definition of the ROI in the images, which will be taken into account for all the duration of the analysis.

After the ROI definition, each image (defined as variable “image”) is converted into the grayscale (defined as “gray_image”) by using the function “rgb2gray(image).” In addition, to adjust the images’ intensity values to the grayscale images, the function “imadjust(gray_image)” is applied. Then, a Gaussian filter is applied to the new images, by using the function “imgaussfilt (gray_image, σ),” to smooth the images and reduce the noise (“filtered_image”). The arguments of this last function are the grayscale images (“gray_image”) to be filtered and sigma (σ = 5), which is the standard deviation of the Gaussian distribution and defines the filter size. The difference between the grayscale and the filtered images contains the noise removed in the filtering phase (“diff_image”). However, the locations of the micro-particles are still visible in these noise images as regions of increased variability. At this point, the new images (“diff_image”) must be converted into binary images (“binary_image”), by using the function “imbinarize(diff_image, th1),” which creates binary images by selecting a threshold value automatically and variable at each circumstance (“th1 = graythresh(diff_image”)). All the values above the threshold will be replaced with 1 and all the others with 0. As mentioned before, the threshold (“th1”) is not a fixed value, but changes for every image, and it is calculated through the function “graythresh(diff_image).” Finally, the function “bwboundaries (binary_image,“noholes”)” was used to trace the exterior boundaries of objects in the binary images. The arguments of this function are binary images (“binary_image”) and the “noholes” option, which specifies searching only the boundaries of objects by excluding noholes, providing better performance. The function returns a cell array (“[B,L,N]”) with the boundaries pixel locations (“B”), a label matrix (“L”) where the objects are labeled and the number of micro-particles found (“N”). After that, a check on the detected micro-particles is carried out, to eliminate possible artifacts. With the function “regionprops (L,“Area,”“Centroid”),” it is possible to measure some micro-particle properties such as the area, the center, and the circularity. Therefore, it is possible to verify if the detected particles have an appropriate area, consistent with the micro-particle size investigated, defining the minimum and maximum dimensions of the searched objects in pixels, to count among the found micro-particles only those that have an appropriate size. For the silica beads and the yeast cells, the minimum area was set to 1 pixel and the maximum area to 2 pixels. For the human cells, the minimum area to 3 pixels and the maximum area to 4 pixels. There is another threshold parameter (“th2”) that needs to be set based on the shape of the objects. In the experimental campaigns carried out, due to the circular geometry of the micro-particles investigated, the threshold parameter (“th2”) was set to 1, to indicate a perfect circle. It is possible to set this threshold differently based on the requirement of the analysis. After defining this parameter, the exterior boundaries of particles are traced and the number of particles is found.

Using the presented algorithm, the same for all the micro-particles investigated, the detection of micro-particles results to be simple, fast, and accurate.

D. Micro-particle DPIV-based algorithm

The data acquired in video format were processed by a DPIV-based automatic algorithm to have instantaneous velocity measurements and visualizations. The time-varying velocity vector maps obtained, showing the displacements of the particles in time in an investigated area, were then processed to extract the mean of the migration velocity per experiment. Thanks to this approach, the complexity of the standard Flow Cytometer equipment is shifted in the algorithm implementation.

Initially, each video is decomposed into frames and a specific ROI is set. The ROI is the portion of the monitored area that was considered for the hydrodynamic cell flow investigation. The ROI was set equal for the experiments using the same cells. The DPIV analysis was conducted by a three-passes discrete Fourier transform (DFT) in frequency domain as implemented by the PIVlab tool.4646. W. Thielicke and E. J. Stamhuis, “PIVlab towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB,” J. Open Res. Software 2(1), e30 (2014). https://doi.org/10.5334/jors.bl The three interrogation areas in pixel were chosen as follows: Area1=64, Area2=32, and Area3=16. The step size of the sampling window used in the DPIV method to calculate the velocities of the micro-particles was set to half of the last interrogation area (Area3 = 16 pixels), resulting in a step size of 8 pixels. The details of the DPIV setting have already been presented by the authors in Ref. 3030. F. Cairone, D. Ortiz, P. J. Cabrales, M. Intaglietta M, and M. Bucolo, “Emergent behaviors in RBCs flows in micro-channels using digital particle image velocimetry,” Microvasc. Res. 116, 77–86 (2018). https://doi.org/10.1016/j.mvr.2017.09.003.In Fig. 5, the algorithm steps from the extraction of the video frames to the computation of the micro-particle velocity trends are presented. On the left three frames, one per cell type are reported, respectively, for the yeast cells (5μm), the human cells (16μm), and the silica beads (6μm). The ROI selected is highlighted in yellow. On the right, for the human cells, a frame at a time instant t¯ of the time-varying velocity vector map V(i,j,t¯) with i and j referring to the ithapex and jthapex pixel position in the image ROI, obtained by the DPIV processing, is considered. The velocity spatial distribution on the horizontal and vertical directions are Vx(i,j,t¯)