In the present work, in vitro blood flowing through bifurcating microchannels was studied, with the aim of characterizing the cell-free layer (CFL). The original images were obtained by means of a high-speed video microscopy system and then processed in MatLab using the Image Processing
Toolbox. The numerical data was obtained automatically and analyzed by optimization techniques using the genetic algorithm approach. The results suggest that the CFL were formed in a similar way at the upper and lower regions in all bifurcations, and the measurements can be approximated
through a sum of trigonometric functions

Bento, David

Lima, R.

Pereira, Ana I.

Pinho, Diana

Taboada, Bruna Rafaela Pereira

Lima, Rui A.

Biblioteca Digital do IPB

IO 2013 | XVI Congresso da Associação Portuguesa de Investigação Operacional 341Cell-free Layer Measurements in BifurcatingMicrochannels: a global approachB. Taboada∗, D. Bento∗, D. Pinho∗, A.I. Pereira‡, R. Lima∗∗Instituto Politécnico de Bragança, Portugal & CEFT, Faculty of Engineering at University of Porto,Portugal.E-mail:{ brunataboada,davidbento,diana,ruimec}@ ipb. pt‡ Instituto Politécnico de Bragança, Portugal & Algoritmi, Universidade do Minho, Portugal.E-mail:apereira@ ipb. ptAbstractIn the present work, in vitro blood flowing through bifurcating microchannels was studied, withthe aim of characterizing the cell-free layer (CFL). The original images were obtained by means ofa high-speed video microscopy system and then processed in MatLab using the Image ProcessingToolbox. The numerical data was obtained automatically and analyzed by optimization techniquesusing the genetic algorithm approach. The results suggest that the CFL were formed in a similarway at the upper and lower regions in all bifurcations, and the measurements can be approximatedthrough a sum of trigonometric functions.Keywords: Cell-free Layer. Image Processing. Nonlinear Optimization. Global Optimization.1 IntroductionBlood flow in microcirculation shows several hemodynamic phenomena that happen at both, in vivoand in vitro blood flowing. Hence, over the years in vitro blood studies in microchannels have beenextensively performed in order to obtain an understanding of blood rheology and its flow dynamics[Goldsmith et al., 1989, Pires et al., 1992, Lima et al., 2012]. A well known hemodynamic phenomenonobserved in both studies, in vivo and in vitro, states that for narrow microtubes (< 300 µm) both hema-tocrit (Hct) and apparent blood viscosity decreases as the tube diameter is reduced [Goldsmith et al., 1989,Pires et al., 1992, Lima et al., 2012]. The physical reasons for these phenomena and for the formationof the cell-free layer (CFL), is known as Fahraeus-Lindqvist effect that is the tendency of red bloodcells (RBCs) to migrate toward the centre of the microtube resulting in a marginal CFL at regionsadjacent to the wall [Caro et al., 1978]. Recently several studies showed strong evidence that the for-mation of the CFL is affected by the geometry of the microchannel [Pinho, 2011, Lima et al., 2008a,Lima et al., 2008b, Leble et al., 2011] and the physiological conditions of the working fluid, such as thehematocrit [Garcia et al., 2012, Fujiwara et al., 2009].Although there have been several studies on the measurement of CFL thickness [Namgung et al., 2010,Kim et al., 2006] according to our knowledge there have been very few studies on the determination ofCFL measurements [Bento et al., 2012, Bento et al., 2013]. For these studies image analysis is extremelyimportant to obtain crucial information [Pinho et al., 2012].The main purpose of the present work is to measure the CFL in a microchannels with bifurcationsby means of an automatic method developed in MatLab [Bento et al., 2012, Bento et al., 2013], andcharacterize the CFL along this microchannel using global optimization techniques.The paper is organized as follows. The Section 2 presents the materials used in this work and themethods that were applied in this study. The Section 3 presents a brief description of the geneticalgorithm. The Section 4 presents the numerical results and some discussion. The last section presentssome conclusions and future work.2 Materials and Methods2.1 Experimental set-upThe high-speed video microscopy system used in this study consists of an inverted microscope (IX71;Olympus) combined with a high-speed camera (i-SPEED LT). The microchannel was placed on the stage342 IO 2013 | XVI Congresso da Associação Portuguesa de Investigação Operacionalof the inverted microscope and by using a syringe pump (PHD ULTRA) a pressure-driven flow was keptconstant (cf. Figure 1).Figure 1: High-speed video microscopy system used in this staudy.The series of microscope images were captured with a resolution of 600 × 800 pixels. All the imageswere recorded at the center plane of the microchannels at a rate of 200 frames/second and were transferredto the computer and then evaluated using image analysis techniques.2.2 Working fluids and microchannel geometryThe blood samples used were collected from a healthy adult sheep, and ethylenediaminetetraacetic acid(EDTA) was added to prevent coagulation. The red blood cells (RBCs) were separated from the bloodby centrifugation and washed twice with physiological saline (PS). The washed RBCs were suspended inDextran 40 (Dx 40) to make up the required RBCs concentration by volume - hematocrit. In this studythe Hct of 10% was used. All blood samples were stored hermetically at 4◦C until the experiment wasperformed.The microchannels fabricated for the proposed study have been produced in PDMS by a soft-lithography technique. The geometry used is a network of microchannels, containing several bifurcationsand confluences. Figure 2 illustrates the configuration of the network and the regions where the CFL wasmeasured.Figure 2: The geometry of the network and the regions where the CFL was measured.2.3 Image AnalysisAll image sequences, like Figure 3, were processed using Image Processing toolbox, available in MatLab[Matlab, 2002], and an automatic method was developed and tested [Bento et al., 2013]. The methodconsists in the combination of binarization of all images sequence and evaluation of all pixels using themaximum intensity.Firstly a median filter with a 3×3 pixel mask was applied to each frame to reduce the noise, and then,the intensity of each pixel in the frame sequence was evaluated to obtain an image with the maximumintensity, as is possible to observe in Figure 4.IO 2013 | XVI Congresso da Associação Portuguesa de Investigação Operacional 343Figure 3: The original image of blood sample flowing in a bifurcating microchannel.Figure 4: The image after the evaluation with the maximum intensity.With this last step it is possible to identify the region of the concentration of blood cells (RBC core)and the region where blood cells do not exist, the cell-free layer. As the final step the image (Figure 4)was converted into a binary image. Finally, the region of interest is selected and the upper and lowerCFLs are automatically measured. Figure 5 represents the image after binarization.Figure 5: Binary image which shows clearly the boundary of CFL and RBC core.3 Global optimization method: Genetic AlgorithmIn the present work the genetic algorithm (GA) was used. The GA is an optimization technique based onthe principles of evolution, this method allows to find a global minimum in a large search space. Givenan individual, that is defined by the genes, this method creates new generations through analysis of theindividuals genes from previous generations and selecting the best ones by applying the fitness function.The GA uses crossover process, where the genes of the best individuals are crossed with genes fromother individuals which also have good performance. The GA also applies the concept of mutation, im-proving the optimization process by introduction values that were not present in the previous generations.This technique does not guarantee that the global minimum is found, however it is accepted that thefinal solution is close to the global minimum provided that successive generations cannot produce betterindividuals [Catlin et al., 2011].344 IO 2013 | XVI Congresso da Associação Portuguesa de Investigação Operacional4 Results and DiscussionThe captured videos were analyzed and the numerical data was taken in the regions already defined inFigure 2. The flow rate used was 500 nl/min and one fluid was studied with 10% of Hct.To fit the numerical data the nonlinear least squares theory was used. In each region Ui, for i =1, ..., 10, and Li, for i = 1, ..., 10, we applied the nonlinear optimization problem defined as followsmin f(y) ≡NR∑k=1(Mk − gh(y, xk))2s.t gh(y, xk) ≥ 0 ∀k = 1, ..., NR(4.1)where (xk,Mk), for k = 1, ..., NR are the CFL measurements of the region R (defined as Ui and Li, fori = 1, ..., 10). The functions gh, for h = 1, ..., 3, are defined as followsg1(y, x) = y1x2 + y2x+ y3,g2(y, x) = y1x+ y2,g3(y, x) = sin(y1x) + cos(y2x) + y3.(4.2)The following table presents the obtained numerical results using the genetic algorithm to solve theoptimization problem (4.1). Since the genetic algorithm is a stochastic method, each problem was solved30 times. Table 1 presents the regions where the problem (4.1) was applied, the average of the optimumvalue and the minimum value obtained in the all 30 runs.Table 1: Numerical results obtained using genetic algorithm.Upper cell-free layer Lower cell-free layerRegion Function Average Minimun Region Function Average MinimunU1 g1 2.71× 107 8.14× 103 L1 g1 1.13× 107 1.05× 105g2 2.17× 103 1.91× 103 g2 1.41× 103 1.34× 103g3 1.90× 103 1.50× 103 g3 1.19× 103 1.00× 103U2 g1 4.29× 107 2.86× 103 L2 g1 4.63× 106 2.36× 103g2 1.27× 103 4.02× 102 g2 2.32× 103 2.07× 103g3 7.68× 102 5.38× 102 g3 2.31× 103 1.85× 103U3 g1 1.32× 108 5.99× 103 L3 g1 9.30× 106 3.44× 103g2 4.76× 103 1.67× 103 g2 3.34× 103 3.06× 103g3 1.92× 103 1.60× 103 g3 2.81× 103 2.36× 103U4 g1 2.88× 106 1.14× 104 L4 g1 4.61× 107 9.63× 104g2 1.27× 103 1.21× 103 g2 5.97× 103 5.18× 103g3 9.94× 102 7.75× 102 g3 4.61× 103 4.07× 103U5 g1 1.30× 107 1.68× 103 L5 g1 1.28× 107 2.26× 103g2 1.77× 103 1.62× 103 g2 2.38× 103 2.04× 103g3 1.43× 103 1.20× 103 g3 3.74× 103 3.35× 103U6 g1 2.61× 106 2.66× 103 L6 g1 8.35× 106 5.49× 103g2 6.07× 102 5.02× 102 g2 9.12× 103 5.46× 103g3 3.70× 102 3.31× 102 g3 1.31× 103 9.90× 102U7 g1 1.18× 107 3.73× 104 L7 g1 6.90× 105 3.53× 103g2 8.65× 102 6.53× 102 g2 4.91× 103 2.71× 103g3 6.45× 102 5.28× 102 g3 3.30× 103 2.55× 103U8 g1 1.53× 107 1.20× 104 L8 g1 3.32× 107 8.49× 104g2 2.72× 103 1.62× 103 g2 2.96× 103 1.31× 103g3 1.82× 103 1.34× 103 g3 3.90× 103 2.76× 103U9 g1 1.58× 108 2.73× 103 L9 g1 2.10× 108 7.36× 104g2 1.24× 103 9.09× 102 g2 1.52× 103 9.08× 102g3 1.10× 103 8.30× 102 g3 1.59× 103 1.09× 103U10 g1 1.21× 107 1.64× 104 L10 g1 2.29× 108 3.08× 103g2 2.03× 103 1.74× 103 g2 3.04× 103 2.41× 103g3 1.77× 103 1.38× 103 g3 2.19× 103 1.81× 103IO 2013 | XVI Congresso da Associação Portuguesa de Investigação Operacional 345The numerical results suggested that the function g3 fits better the CFL boundary, since the minimumvalue was obtained for this function. Other important fact is that the boundary has the same behaviorin all bifurcations. The only exception was verified in the regions L5, L8 and L9, in these regions thebest fit was obtained with the function g2.5 Conclusions and Future WorkIn this study, we present a method to obtained automatically the CFL measurements. The CFL boundarywas fitted using three different functions. The genetic algorithm was used to solve the constrainedoptimization problem. The best fit was obtained using the function g3, i.e. a sum of trigonometricfunctions. As future work, we will test more fluids with different properties and different functions to fitthe CFL measurements.AcknowledgmentsThe authors acknowledge the financial support provided by: PTDC/SAU-BEB/108728/2008, PTDC/SAU-BEB/105650/2008, PTDC/EME-MFE/099109/2008 and PTDC/SAU-ENB/116929/2010 from FCT (Sci-ence and Technology Foundation), COMPETE, QREN and European Union (FEDER).References[Bento et al., 2013] Bento, D., Pinho, D., Pinto, E., Tomoko, Y., Correia, T., Lima, J., Pereira, A.I.,Lima, R. (2013). Cell-free layer measurements in a bifurcation microchannel: comparison between amanual and automatic methods. 5th Portuguese Congress on Biomechanics: 359-362.[Bento et al., 2012] Bento, D., Pinho, D., Pereira, A., Lima, R. (2012) Cell-Free Layer (CFL) Analysisin a Glass Capillary: Comparison Between a Manual and Automatic Method. AIP ConferenceProceedings 1479: 786-789.[Caro et al., 1978] Caro, C., Pedley, T., Schroter, R., Seed, W. (1978). The mechanics of the circulation.Oxford University Press.[Catlin et al., 2011] Catlin, G., Advani, S., Prasad, A. (2011). Optimization of polymer electrolyte mem-brane fuel cell channels using a genetic algorithm. Journal of Power Sources, 196:9407–9418.[Fujiwara et al., 2009] Fujiwara, H., Ishikawa, T., Lima, R., Matsuki, N., Imai, Y., Kaji, H., Nishizawa,M., Yamaguchi, T. (2009). Red blood cells motions in high-hematocrit blood flowing through astenosed microchannel. Journal of Biomechanics, 42:838–843.[Garcia et al., 2012] Garcia, V., Dias, R., Lima R. (2012). In Vitro Blood Flow Behaviour in Microchan-nels with Simple and Complex Geometries. Journal of Biomechanics Applied Biological Engineering- Principles and Practice, Ganesh R. Naik (ed.), InTechcs, 17:394–416.[Goldsmith et al., 1989] Goldsmith, H., Cokelet, G., Gaehtgens, P. (1989). Robin Fahraeus: evolution ofhis concepts in cardiovascular physiology. American Journal of Physiology, 257:H1005–H10015.[Kim et al., 2006] Kim, S., Kong, R. L., Popel, A. S., Intaglietta, M., Jonhson J. C.(2006). A computer-based method for determination of the cell-free layer width in microcirculation. Microcirculation,13:199-207.[Leble et al., 2011] Leble, V., Lima, R., Dias, R. P., Fernandes, C. S., Ishikawa, T., Imai, Y., Yamaguchi,T. (2011). Asymmetry of red blood cell motions in a microchannel with a diverging and convergingbifurcation. Biomicrofluidics, 5:044120.[Lima et al., 2008a] Lima, R., Wada, S., Tanak, S., Takeda, M. (2008). In vitro blood flow in a rectangularPDMS microchannel: experimental observations using a confocal micro-PIV system. BiomedicalMicrodevices, 10(2):153–167.[Lima et al., 2008b] Lima, R., Ishikawa, T., Imai, Y. (2008). Radial dispersion of red blood cells inblood flowing through glass capillaries: role of hematocrit and geometry. Journal of Biomechanics,41:2188-2197.346 IO 2013 | XVI Congresso da Associação Portuguesa de Investigação Operacional[Lima et al., 2012] Lima, R., Ishikawa, T., Imai, Y., Yamaguchi, T. (2012) Single and two-phase flowson Chemical and Biomedical Engineering. Bentham Science, Dias et al., 513-547.[Matlab, 2002] Eddins, S. L., Gonzalez, R. C., Woods, R. E. (2002). Digital Image Processing UsingMatlab. MathWorks.[Namgung et al., 2010] Namgung, B., Ong, P. K., Wong, Y. H., Lim, D., Chun, K. C., Kim, S. (2010). Acomparative study of histogram-based thresholding methods for the determination of cell-free layerwidth in small blood vessels. Physiological Measurement, 31:N61–N70.[Pinho, 2011] Pinho, D. (2011). Determination and characterization of red blood cells trajectories: a semi-automatic method. Master in Biomedical Technology, Polytechnic Institute of Bragança, Portugal,2011 (in portuguese).[Pinho et al., 2012] Pinho, D., Lima, R., Pereira, A. I., Gayubo, F. (2012). Automatic tracking of la-beled red blood cells in microchannels. International Journal for Numerical Methods in BiomedicalEngineering, DOI: 10.1002/cnm.[Pires et al., 1992] Pires, A. A., Neuhaus, D., Gaehtgens P. (1992). Blood viscosity in tube flow: depen-dence on diameter and hematocrit. American Journal of Physiology, 263:H1770–H1778.

Cell-free layer measurements in bifurcating microchannels: a global approach

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Cell-free layer measurements in bifurcating microchannels: a global approach

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