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Numerical simulation of a single cell passing through a narrow slit

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Abstract

The narrow slit between endothelial cells that line the microvessel wall is the principal pathway for tumor cell extravasation to the surrounding tissue. To understand this crucial step for tumor hematogenous metastasis, we used dissipative particle dynamics method to investigate an individual cell passing through a narrow slit numerically. The cell membrane was simulated by a spring-based network model which can separate the internal cytoplasm and surrounding fluid. The effects of the cell elasticity, cell shape, nucleus and slit size on the cell transmigration through the slit were investigated. Under a fixed driving force, the cell with higher elasticity can be elongated more and pass faster through the slit. When the slit width decreases to 2/3 of the cell diameter, the spherical cell becomes jammed despite reducing its elasticity modulus by 10 times. However, transforming the cell from a spherical to ellipsoidal shape and increasing the cell surface area by merely 9.3 % can enable the cell to pass through the narrow slit. Therefore, the cell shape and surface area increase play a more important role than the cell elasticity in cell passing through the narrow slit. In addition, the simulation results indicate that the cell migration velocity decreases during entrance but increases during exit of the slit, which is qualitatively in agreement with the experimental observation.

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References

  • Albelda SM, Smith CW, Ward PA (1994) Adhesion molecules and inflammatory injury. Faseb J 8:504–512

    Google Scholar 

  • Boey SK, Boal DH, Discher DE (1998) Simulations of the erythrocyte cytoskeleton at large deformation. I Microsc Models Biophys J 75:1573–1583

    Google Scholar 

  • Chaw KC, Manimaran M, Tay EH, Swaminathan S (2007) Multi-step microfluidic device for studying cancer metastasis. Lab Chip 7:1041–1047

    Article  Google Scholar 

  • Chaw KC, Manimaran M, Tay FEH, Swaminathan S (2006) A quantitative observation and imaging of single tumor cell migration and deformation using a multi-gap microfluidic device representing the blood vessel. Microvasc Res 72:153–160

    Article  Google Scholar 

  • Chen MB, Whisler JA, Jeon JS, Kamm RD (2013) Mechanisms of tumor cell extravasation in an in vitro microvascular network platform. Integr Biol UK 5:1262–1271

    Article  Google Scholar 

  • Cross SE, Jin YS, Rao J, Gimzewski JK (2007) Nanomechanical analysis of cells from cancer patients. Nat Nanotechnol 2:780–783

    Article  Google Scholar 

  • Dao M, Li J, Suresh S (2006) Molecularly based analysis of deformation of spectrin network and human erythrocyte. Mat Sci Eng C Bio S 26:1232–1244

    Article  Google Scholar 

  • Dewitt S, Hallett M (2007) Leukocyte membrane “expansion”: a central mechanism for leukocyte extravasation. J Leukoc Biol 81:1160–1164

    Article  Google Scholar 

  • Espanol P (1995) Hydrodynamics from dissipative particle dynamics. Phys Rev E 52:1734–1742

    Article  MathSciNet  Google Scholar 

  • Fan J, Fu BM (2015) Quantification of malignant breast cancer cell MDA-MB-231 transmigration across brain and lung microvascular endothelium. Ann Biomed Eng. doi:10.1007/s10439-015-1517-y

  • Fan XJ, Phan-Thien N, Chen S, Wu XH, Ng TY (2006) Simulating flow of DNA suspension using dissipative particle dynamics. Phys Fluids 18(6):063102

    Article  MATH  Google Scholar 

  • Fedosov DA, Caswell B, Karniadakis GE (2010) Systematic coarse-graining of spectrin-level red blood cell models. Comput Method Appl M 199:1937–1948

    Article  MathSciNet  MATH  Google Scholar 

  • Fedosov DA, Gompper G (2014) White blood cell margination in microcirculation. Soft Matter 10:2961–2970

    Article  Google Scholar 

  • Freund JB (2013) The flow of red blood cells through a narrow spleen-like slit. Phys Fluids 25(11):110807

    Article  Google Scholar 

  • Fushimi K, Verkman AS (1991) Low viscosity in the aqueous domain of cell cytoplasm measured by picosecond polarization microfluorimetry. J Cell Biol 112:719–725

    Article  Google Scholar 

  • Groot RD, Warren PB (1997) Dissipative particle dynamics: bridging the gap between atomistic and mesoscopic simulation. J Chem Phys 107:4423–4435

    Article  Google Scholar 

  • Guo HL et al (2004) Mechanical properties of breast cancer cell membrane studied with optical tweezers. Chin Phys Lett 21:2543–2546

    Article  Google Scholar 

  • Helfrich W (1973) Elastic properties of lipid bilayers: theory and possible experiments. Z Naturforsch C C 28:693–703

    Google Scholar 

  • Hoogerbrugge PJ, Koelman JMVA (1992) Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys Lett 19:155–160

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Leong FY, Li QS, Lim CT, Chiam KH (2011) Modeling cell entry into a micro-channel. Biomech Model Mechanobiol 10:755–766

    Article  Google Scholar 

  • Li J, Dao M, Lim CT, Suresh S (2005) Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte. Biophys J 88:3707–3719

    Article  Google Scholar 

  • Li QS, Lee GYH, Ong CN, Lim CT (2008) AFM indentation study of breast cancer cells. Biochem Bioph Res Commun 374:609–613

    Article  Google Scholar 

  • Li X, Peng Z, Lei H, Dao M, Karniadakis GE (2014) Probing red blood cell mechanics, rheology and dynamics with a two-component multi-scale model. Philos Trans Ser A Math Phys Eng Sci 372. doi:10.1098/rsta.2013.0389

  • Lincoln B et al (2004) Deformability-based flow cytometry. Cytom Part A 59A:203–209

    Article  Google Scholar 

  • McDonald DM, Baluk P (2002) Significance of blood vessel leakiness in cancer. Cancer Res 62:5381–5385

    Google Scholar 

  • Mierke CT (2011) Cancer cells regulate biomechanical properties of human microvascular endothelial cells. J Biol Chem 286:40025–40037

    Article  Google Scholar 

  • Mierke CT (2012) Endothelial cell’s biomechanical properties are regulated by invasive cancer cells. Mol Biosyst 8:1639–1649

    Article  Google Scholar 

  • Miles FL, Pruitt FL, van Golen KL, Cooper CR (2008) Stepping out of the flow: capillary extravasation in cancer metastasis. Clin Exp Metastasis 25:305–324

    Article  Google Scholar 

  • Omori T, Hosaka H, Imai Y, Yamaguchi T, Ishikawa T (2014) Numerical analysis of a red blood cell flowing through a thin micropore. Phys Rev E 89(1):013008

    Article  Google Scholar 

  • Pan DY, Nhan PT, Nam MD, Khoo BC (2013) Numerical investigations on the compressibility of a DPD fluid. J Comput Phys 242:196–210. doi:10.1016/j.jcp.2013.02.013

    Article  Google Scholar 

  • Park S, Ang RR, Duffy SP, Bazov J, Chi KN, Black PC, Ma HS (2014) Morphological differences between circulating tumor cells from prostate cancer patients and cultured prostate cancer cells. Plos One 9(1):e85264

    Article  Google Scholar 

  • Pivkin IV, Karniadakis GE (2008) Accurate coarse-grained modeling of red blood cells. Phys Rev Lett 101(11):118105

    Article  Google Scholar 

  • Quinn DJ, Pivkin I, Wong SY, Chiam KH, Dao M, Karniadakis GE, Suresh S (2011) Combined simulation and experimental study of large deformation of red blood cells in microfluidic systems. Ann Biomed Eng 39:1041–1050

    Article  Google Scholar 

  • Rejniak KA (2012) Investigating dynamical deformations of tumor cells in circulation: predictions from a theoretical model. Front Oncol 2:111. doi:10.3389/fonc.2012.00111

    Article  Google Scholar 

  • Reymond N, d’Agua BB, Ridley AJ (2013) Crossing the endothelial barrier during metastasis. Nat Rev Cancer 13:858–870

    Article  Google Scholar 

  • Schmidschonbein GW, Shih YY, Chien S (1980) Morphometry of human-leukocytes. Blood 56:866–875

  • Soares JS, Gao C, Alemu Y, Slepian M, Bluestein D (2013) Simulation of platelets suspension flowing through a stenosis model using a dissipative particle dynamics approach. Ann Biomed Eng 41:2318–2333

    Article  Google Scholar 

  • Stoletov K, Kato H, Zardouzian E, Kelber J, Yang J, Shattil S, Klemke R (2010) Visualizing extravasation dynamics of metastatic tumor cells. J Cell Sci 123:2332–2341

    Article  Google Scholar 

  • Strell C, Entschladen F (2008) Extravasation of leukocytes in comparison to tumor cells. Cell Commun Signal CCS 6:10. doi:10.1186/1478-811X-6-10

    Article  Google Scholar 

  • Sugihara-Seki M, Fu BMM (2005) Blood flow and permeability in microvessels. Fluid Dyn Res 37:82–132

    Article  MathSciNet  MATH  Google Scholar 

  • Suresh S (2007) Biomechanics and biophysics of cancer cells. Acta Biomater 3:413–438

    Article  MathSciNet  Google Scholar 

  • Voura EB, Sandig M, Siu CH (1998) Cell-cell interactions during transendothelial migration of tumor cells. Microsc Res Tech 43:265–275

    Article  Google Scholar 

  • Warren PB (2003) Vapor-liquid coexistence in many-body dissipative particle dynamics. Phys Rev E 68(6):066702

    Article  Google Scholar 

  • Weiss L, Orr FW, Honn KV (1988) Interactions of cancer-cells with the microvasculature during metastasis. Faseb J 2:12–21

    Google Scholar 

  • Wirtz D, Konstantopoulos K, Searson PC (2011) The physics of cancer: the role of physical interactions and mechanical forces in metastasis. Nat Rev Cancer 11:512–522. doi:10.1038/nrc3080

    Article  Google Scholar 

  • Wu TH, Feng JJ (2013) Simulation of malaria-infected red blood cells in microfluidic channels: passage and blockage. Biomicrofluidics 7(4):044115

    Article  MathSciNet  Google Scholar 

  • Yan WW, Cai B, Liu Y, Fu BM (2012) Effects of wall shear stress and its gradient on tumor cell adhesion in curved microvessels. Biomech Model Mech 11:641–653

    Article  Google Scholar 

  • Ye T, Phan-Thien N, Khoo BC, Lim CT (2014) Dissipative particle dynamics simulations of deformation and aggregation of healthy and diseased red blood cells in a tube flow. Phys Fluids 26(11):111902

    Article  Google Scholar 

  • Zhang ZF, Xu J, Hong B, Chen XL (2014) The effects of 3D channel geometry on CTC passing pressure-towards deformability-based cancer cell separation. Lab Chip 14:2576–2584

    Article  Google Scholar 

  • Zhu C, Bao G, Wang N (2000) Cell mechanics: mechanical response, cell adhesion, and molecular deformation. Annu Rev Biomed Eng 2:189–226

    Article  Google Scholar 

Download references

Acknowledgments

Supports given by HKRGC PolyU 5202/13E, PolyU G-YL41, NSFC 51276130, and NIH SC1 CA153325-01 are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong

    L. L. Xiao & Y. Liu

  2. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China

    L. L. Xiao & S. Chen

  3. Department of Biomedical Engineering, The City College of the City University of New York, New York, NY, USA

    B. M. Fu

Authors
  1. L. L. Xiao
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  2. Y. Liu
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  3. S. Chen
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  4. B. M. Fu
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Correspondence to Y. Liu.

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Xiao, L.L., Liu, Y., Chen, S. et al. Numerical simulation of a single cell passing through a narrow slit. Biomech Model Mechanobiol 15, 1655–1667 (2016). https://doi.org/10.1007/s10237-016-0789-y

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  • DOI: https://doi.org/10.1007/s10237-016-0789-y

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