Abstract
This chapter covers dimensionless evaluation for the stiffness-based deformability of a cell using a high-resolution vision system and a microchannel. In conventional approaches, the transit time of a cell through a microchannel is often utilized for the evaluation of cell deformability. However, such time includes both the information of cell stiffness and viscosity. In this work, we eliminate the effect from cell viscosity, and focus on the cell stiffness only. We find that the velocity of a cell varies when enters a channel, and eventually reaches to equilibrium where the velocity becomes constant. The constant velocity is defined as the equilibrium velocity of the cell, and it is utilized to define the observability of stiffness-based deformability. The necessary and sufficient numbers of sensing points for evaluating stiffness-based deformability are discussed. Through the dimensional analysis on the microchannel system, three dimensionless parameters determining stiffness-based deformability are derived, and a new index is introduced based on these parameters. The experimental study is conducted on the red blood cells from a healthy subject and a diabetic patient. With the proposed index, we showed that the experimental data can be nicely arranged.
Keywords
Part of the materials in this chapter is from C. Tsai, S. Sakuma, F. Arai and M. Kaneko, IEEE Transactions on Biomedical Engineering, vol.61, no.4, pp1187-1195, 2014. The permission of reuse is granted by IEEE.
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Notes
- 1.
The time-dependent property of viscosity is sometimes referred as rate-dependant.
- 2.
The width of 4.0 μm is chosen since RBCs are generally ranged from 6–8 μm in diameter. The microchannel should be narrow enough to deform the cell but not too narrow to cause damages. Moreover, based on our experience, RBCs are easily stuck in the microchannels with width 3 μm or less.
- 3.
see Appendix A for the details of how physical quantities are obtained.
- 4.
fluid velocity here represent the velocity of fluid inside the channel when there is no cell in the channel. The fluid velocity is estimated based on the velocity profile as the method described in [31].
- 5.
the value of 4 is obtained by subtracting the rank, 3, from the total number of dimensional quantities, 7.
- 6.
Here we consider cell deformability as the easiness of a cell to be deformed. Thus, high deformability reflects low stiffness and vice versa.
References
Bow H, Pivkin IV, Diez-Silva M, Goldfless SJ, Dao M, Suresh S, Niles JC, Han J (2011) A microfabricated deformability-based flow cytometer with application to malaria. Lab Chip 11:1065–1073
Glenister FK, Coppel RL, Cowman AF, Mohandas N, Cooke BM (2002) Contribution of parasite proteins to altered mechanical properties of malaria-infected red blood cells. Blood 99(3):1060–1063
Baskurt OK, Gelmont D, Meiselman HJ (2003) Red blood cell deformability in sepsis. Am J Respir Critical Care Med 157(2):421–427
Tsukada K, Sekizuka E, Oshio C, Minamitani H (2001) Direct measurement of erythrocyte deformability in diabetes mellitus with a transparent microchannel capillary model and high-speed video camera system. Microvasc Res 61:231–239
Brandao M, Fontes A, Barjas-Castro M, Barbosa L, Costa F, Cesar C, Saad S (2003) Optical tweezers for measuring red blood cell elasticity: application to the study of drug response in sickle cell disease. Eur J Hematol 70:207–211
Zheng Y, Shojaei-Baghini E, Azad A, Wang C, Sun Y (2012) High-throughput biophysical measurement of human red blood cells. Lab Chip 12:2560–2567
Hou HW, Li QS, Lee GYH, Kumar AP, Ong CN, Lim CT (2009) Deformability study of breast cancer cells using microfluidics. Biomed Microdevices 11:557–564
Adamo A, Sharei A, Adamo L, Lee B, Mao S, Jensen KF (2012) Microfluidics-based assessment of cell deformability. Anal Chem 84:6438–6443
Rosenbluth MJ, Lam WA, Fletcher DA (2008) Analyzing cell mechanics in hematologic disease with microfluidic biophysical flow cytometry. Lab Chip 8:102–1070
Carlo DD (2012) A mechanical biomarker of cell state in medicine. J Lab Autom 17(1):32–42
Roth KB, Eggleton CD, Neeves KB, Marr DWM (2013) Measuring cell mechanics by optical alignment compression cytometry. Lab Chip 13(8):1571–1577
Tan Y, Sun D, Wang J, Huang W (2010) Mechanical characterization of human red blood cells under different osmotic conditions by robotic manipulation with optical tweezers. IEEE Trans Biomed Eng 57(7):1816–1825
Tomaiuolo G, Barra M, Preziosi V, Cassinese A, Rotoli B, Guido S (2010) Microfluidics analysis of red blood cell membrane viscoelasticity. Lab Chip 11:449–454
Zhang H, Liu K (2008) Optical tweezers for single cells. J Royal Soci Interface 5:671–690
Lee GYH, Lim CT (2007) Biomechanics approaches to studying human diseases. Trends Biotechnol 25(3):111–118
Wojcikiewicz EP, Zhang X, Moy VT (2004) Force and compliance measurements on living cells using atomic force microscopy (afm). Biological Proc Online 6:1–9
Binnig G, Quate CF, Gerber C. Atomic force microscope. Phys Rev Lett 56(9):930–933
Radmacher M, Fritz M, Kacher CM, Cleveland JP, Hansma PK (1996) Measuring the viscoelastic properties of human platelets with the atomic force microscope. Biophys J 70:556–567
Dao M, Lim CT, Suresh S (2003) Mechanics of the human red blood cell deformed by optical tweezers. J Mech Phys Solids 51:2259–2280
Worthen GS, Schwab B 3rd, Elson EL, Downey GP (1989) Mechanics of stimulated neutrophils: cell stiffening induces retention in capillaries. Science 245(4914):183–186
Isermann P, Davidson PM, Sliz JD, Lammerding J (2012) Assays to measure nuclear mechanics in interphase cells. Curr Prot Cell Biol 56(22.16):1–21
Youn S, Lee DW, Cho Y (2008) Cell-deformability-monitoring chips based on strain-dependent cell-lysis rates. J Microelectromech Syst 17(2):302–308
Byun S, Son S, Amodei D, Cermak N, Shaw J, Kang JH, Hercht VC, Winslow MM, Jacks T, Mallick P, Manalis S (2013) Characterizing deformability and surface friction of cancer cells. Proc Natl Acad Sci PNAS 110(19):7580–7585
Gossett DR, Tse HTK, Lee SA, Ying Y, Lindgren AG, Yang OO, Rao J, Clark AT, Carlo DD (2012) Hydrodynamic stretching of single cells for large population mechanical phenotyping. PNAS 109:7630–7635
Hirose Y, Tadakuma K, Higashimori M, Arai T, Kaneko M, Iitsuka R, Yamanishi Y, Arai F (2010) A new stiffness evaluation toward high speed cell sorter. In Proceedings of the IEEE International Conference on Robotics and Automation, ICRA, pp 4113–4118, Anchorage, USA, May 2010
Tsai CD, Kaneko M, Sakuma S, Arai F (2012) Evaluation of cell impedance using a μ-channel. In Proceedings of the IEEE Engineering in Medicine & Biology Society, EMBC, pp 5518–5521, San Diego, USA, August 2012
Tsai CD, Kaneko M, Sakuma S, Arai F (2012) Phase decomposition of a cell passing through a μ-channel—a method for improving the evaluation of cell stiffness. In Proceedings IEEE International Conference on Mechatronics and Automation, ICMA, pp 138–143, Chengdu, China, August 5–8 2012
Tsai CD, Kaneko M, Sakuma S, Arai F (2012) Enhanced cell stiffness evaluation by two-phase decomposition. In Proceedings of the 16th International Conference on Miniaturized Systems for Chemistry and Life Sciences, μTAS12, pp 1009–1011, Okinawa, Japan, October 2012
Tsai CD, Kaneko M, Sakuma S, Arai F (2013) Observability of cell stiffness in micro-channel method. In Proceedings of the IEEE International Conference on Robotics and Automation, ICRA, pp 2792–2798, Karlsruhe, Germany, May 2013
Fung YC (1993) Biomechanics: mechanical properties of living tissues. Springer-Verlag, New York (http://www.springer.com/gp/book/9780387979472)
Tsai CD, Sakuma S, Kaneko M, Arai F (2013) Normalization of flow-in velocity for improving the evaluation on cell deformability. In Proceedings IEEE International Conference on Mechatronics and Automation, ICMA, pp 261–266, Takamatsu, Japan, August 2013
Elrod HG (1973) Thin-film lubrication theory for newtonian fluids with surfaces possessing striated roughness or grooving. J Lubrication Tech. 95(4):484–489
Gukhman AA (1965) Introduction to the theory of similarity. Academic, New York
Herrmann S, Klaus G (2003) Boundary-layer theory. Springer-Verlag Berlin, (http://www.springer.com/gp/book/9783540662709)
Acknowledgement
We would like to thank Dr. Sakata (M.D. Ph.D.), Dr. Ohtani (M.D. Ph.D.) and Dr. Taniguchi (M.D.) for their help in preparing blood samples from the subjects. This work is supported by The Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan Grant-in-Aid for Scientific Research on Innovative Areas “Bio Assembler”.
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Appendix A Physical Quantities in Microchannel system
Appendix A Physical Quantities in Microchannel system
The model in Thin-Film Lubrication Theory [32] is adopted, and it is claimed that a very thin layer of fluid always exists between two objects. In other words, there is no direct contact between a cell and channel wall, and the interaction always through a thin layer of fluid between them. While a cell through a channel, the resistance, \({{F}_{R}}\), would be the shear force given by
where μ, \({{u}_{eq}}\), dg and \({{A}_{s}}\) are fluid viscosity, equilibrium velocity, gap size, and the area where the force is exerted. By assuming the shape of deformed cell inside the channel is a cylinder, we have
where λ is the cell length inside the channel (a.k.a. in-channel length). \({{d}_{g}}\) can be regarded as a function of the compression force, \({{F}_{c}}\), acting on the cell
where k, \({{D}_{c}}\) and w are cell stiffness, undeformed diameter and channel width, respectively. Thus, we have
On the other hand, the force pushing a cell forward (the pushing force, \({{F}_{P}}\)) is
where ΔP and \({{A}_{C}}\) are the pressure difference between two sides of the channel and cross-sectional area, respectively. \({{A}_{C}}\) is
Because it is difficult to directly measure the ΔP in a microchannel experimentally, fluid velocity is employed for the information of flow. We know that ΔP is a function of fluid velocity, \({{u}_{f}}\) according to Hagen-Poiseuille equation [34], thus we have
From Eqs. (2.28)–(2.30) we have
While a cell reaches equilibrium, the force pushing cell forward, \({{\text{F}}_{P}}\) and backward, \({{\text{F}}_{\text{R}}}\), are balanced, and can be represented by
In summary, we have
which shows that 7 physical quantities, k, \({{D}_{C}}\), λ, ueq, uf, w and μ, determine how a cell moving inside a microchannel.
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Tsai, CH., Sakuma, S., Arai, F., Kaneko, M. (2015). Dimensionless Evaluation of Cell Deformability with High Resolution Positioning in a Microchannel. In: Arai, T., Arai, F., Yamato, M. (eds) Hyper Bio Assembler for 3D Cellular Systems. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55297-0_2
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