Experimental Verification of the Elastic Formula for the Aspirated Length of a Single Cell Considering the Size and Compressibility of Cell During Micropipette Aspiration

Abstract

In this study, an aspiration system for elastic spheres was developed to verify the approximate elastic formula for the aspirated length of a single solid-like cell undergoing micropipette aspiration (MPA), which was obtained in our previous study by theoretical analysis and numerical simulation. Using this system, foam silicone rubber spheres with different diameters and mechanical properties were aspirated in a manner similar to the MPA of single cells. Comparisons between the approximate elastic formula and aspiration experiments of spheres indicated that the predictions of the formula agreed with the experimental results. Additionally, combined with the MPA data of rabbit chondrocytes, differences in terms of the elastic parameters derived from the half-space model, incompressible sphere model, and compressible sphere model were explored. The results demonstrated that the parameter ξ (ξ = R/a, where R is the radius of the cell and a is the inner radius of the micropipette) and Poisson’s ratio significantly influenced the determination of the elastic modulus and bulk modulus of the cell. This work developed for the first time an aspiration system of elastic spheres to study the elastic responses of the MPA of a single cell and provided new evidence supporting the use of the approximate elastic formula to determine cellular elastic parameters from the MPA data.

This is a preview of subscription content, log in to check access.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11

References

  1. 1.

    Ahmad, I. L., and M. R. Ahmad. Trends in characterizing single cell’s stiffness properties. Micro Nano Syst. Lett. 2:8, 2014. https://doi.org/10.1186/s40486-014-0008-5.

    Article  Google Scholar 

  2. 2.

    Baaijens, F. P. T., W. R. Trickey, T. A. Laursen, and F. Guilak. Large deformation finite element analysis of micropipette aspiration to determine the mechanical properties of the chondrocyte. Ann. Biomed. Eng. 33:494–501, 2005.

    Article  PubMed  Google Scholar 

  3. 3.

    Bidhendi, A. J., and R. K. Korhonen. A finite element study of micropipette aspiration of single cells: Effect of compressibility. Comput. Math. Methods Med. 2012. https://doi.org/10.1155/2012/192618.

    PubMed  Article  Google Scholar 

  4. 4.

    Boudou, T., J. Ohayon, Y. Arntz, G. Finet, C. Picart, and P. Tracqui. An extended modeling of the micropipette aspiration experiment for the characterization of the Young’s modulus and Poisson’s ratio of adherent thin biological samples: numerical and experimental studies. J. Biomech. 39:1677–1685, 2006.

    Article  PubMed  Google Scholar 

  5. 5.

    Charras, G. T., P. P. Lehenkari, and M. A. Horton. Atomic force microscopy can be used to mechanically stimulate osteoblasts and evaluate cellular strain distributions. Ultramicroscopy 86:85–95, 2001.

    Article  PubMed  CAS  Google Scholar 

  6. 6.

    Chaudhuri, O., and D. J. Mooney. Stem-cell differentiation: anchoring cell-fate cues. Nat. Mater. 11:568–569, 2012.

    Article  PubMed  CAS  Google Scholar 

  7. 7.

    Fung, Y. C. Biomechanics: Mechanical Properties of Living Tissues. New York: Springer, p. 788, 1993.

    Google Scholar 

  8. 8.

    Galbraith, C. G., and M. P. Sheetz. Forces on adhesive contacts affect cell function. Curr. Opin. Cell Biol. 10:566–571, 1998.

    Article  PubMed  CAS  Google Scholar 

  9. 9.

    Guilak, F., G. Erickson, and H. Ting-Beall. The effects of osmotic stress on the viscoelastic and physical properties of articular chondrocytes. Biophys. J. 82:720–727, 2002.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  10. 10.

    Guz, N., M. Dokukin, V. Kalaparthi, and I. Sokolov. If cell mechanics can be described by elastic modulus: study of different models and probes used in indentation experiments. Biophy. J. 107:564–575, 2014.

    Article  CAS  Google Scholar 

  11. 11.

    Haider, M. A., and F. Guilak. An axisymmetric boundary integral model for incompressible linear viscoelasticity: application to the micropipette aspiration contact problem. ASME J. Biomech. Eng. 122:236–244, 2000.

    Article  CAS  Google Scholar 

  12. 12.

    Haider, M. A., and F. Guilak. An axisymmetric boundary integral model for assessing elastic cell properties in the micropipette aspiration contact problem. ASME J. Biomech. Eng. 124:586–595, 2002.

    Article  Google Scholar 

  13. 13.

    Hochmuth, R. M. Micropipette aspiration of living cells. J. Biomech. 33:15–22, 2000.

    Article  PubMed  CAS  Google Scholar 

  14. 14.

    Hu, W. J., H. Chen, K. Zhang, and X. Chen. Effect of porosity on the properties of open cell silicone rubber foam materials. China Rubber Ind. 45:647–651, 1998; ((In Chinese)).

    CAS  Google Scholar 

  15. 15.

    Jones, W. R., H. P. Ting-Beall, G. M. Lee, S. S. Kelly, R. M. Hochmuch, and F. Guilak. Alterations in the Young’s modulus and volumetric properties of chondrocytes isolated from normal and osteoarthritic human cartilage. J. Biomech. 32:119–127, 1999.

    Article  PubMed  CAS  Google Scholar 

  16. 16.

    Khani, M.-M., M. Tafazzoli-Shadpour, Z. Goli-Malekabadi, and N. Haghighipour. Mechanical characterization of human mesenchymal stem cells subjected to cyclic uniaxial strain and TGF-β1. J. Mech. Behav. Biomed. 43:18–25, 2015.

    Article  CAS  Google Scholar 

  17. 17.

    Kinney, J. H., G. W. Marshall, S. J. Marshall, and D. L. Haupt. Three-dimensional imaging of large compressive deformations in elastomeric foams. J. Appl. Polym. Sci. 80:1746–1755, 2001.

    Article  CAS  Google Scholar 

  18. 18.

    Lee, G. Y. H., and C. T. Lim. Biomechanics approaches to studying human diseases. Trends Biotechnol. 25:111–118, 2007.

    Article  PubMed  CAS  Google Scholar 

  19. 19.

    Lekka, M., and P. Laidler. Applicability of AFM in cancer detection. Nat. Nanotechnol. 4:72–73, 2009.

    Article  PubMed  CAS  Google Scholar 

  20. 20.

    Li, Y. S. Study on the mechanical models for micropipette aspiration of cells. Thesis for the Doctor Degree of Taiyuan University of Technology, pp. 51–52, 2014 (In Chinese).

  21. 21.

    Li, Y. S., and W. Y. Chen. Finite element analysis of micropipette aspiration considering finite size and compressibility of cells. Sci. China Phys. Mech. 56:2208–2215, 2013.

    Article  CAS  Google Scholar 

  22. 22.

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

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  23. 23.

    Loh, O., A. Vaziri, and H. D. Espinosa. The potential of MEMS for advancing experiments and modeling in cell mechanics. Exp. Mech. 49:105–124, 2010.

    Article  CAS  Google Scholar 

  24. 24.

    Maksym, G. N., B. Fabry, J. P. Butler, D. Navajas, D. J. Tschumperlin, J. D. Laporte, and J. J. Fredberg. Mechanical properties of cultured human airway smooth muscle cells from 0.05 to 0.4 Hz. J. Appl. Physiol. 89:1619–1632, 2000.

    Article  PubMed  CAS  Google Scholar 

  25. 25.

    Mills, J. P., L. Qie, M. Dao, C. T. Lim, and S. Suresh. Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers. Mech. Chem. Biosyst. 1:169–180, 2004.

    PubMed  CAS  Google Scholar 

  26. 26.

    Nash, G. B., E. O’Brien, and J. A. Dormandy. Abnormalities in the mechanical properties of red blood cells caused by Plasmodium falciparum. Blood. 74:855–861, 1989.

    PubMed  CAS  Google Scholar 

  27. 27.

    Pachenari, M., S. M. Seyedpour, M. Janmaleki, S. B. Shayan, S. Taranejoo, and H. Hosseinkhani. Mechanical properties of cancer cytoskeleton depend on actin filaments to microtubules content: investigating different grades of colon cancer cell lines. J. Biomech. 47:373–379, 2014.

    Article  PubMed  CAS  Google Scholar 

  28. 28.

    Paszek, M. J., N. Zahir, and V. M. Weaver. Tensional homeostasis and the malignant phenotype. Cancer Cell. 8:241–254, 2005.

    Article  PubMed  CAS  Google Scholar 

  29. 29.

    Roduit, C., S. Sekatski, G. Dietler, S. Catsicas, F. Lafont, and S. Kasas. Stiffness to mography by atomic force microscopy. Biophys. J. 97:674–677, 2009.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  30. 30.

    Sato, M., D. P. Theret, L. T. Wheeler, N. Ohshima, and R. M. Nerem. Application of the micropipette technique to the measurement of cultured porcine aortic endothelial cell viscoelastic properties. ASME J. Biomech. Eng. 112:263–268, 1990.

    Article  CAS  Google Scholar 

  31. 31.

    Seyedpour, S. M., M. Pachenari, M. Janmaleki, M. Alizadeh, and H. Hosseinkhani. Effects of an antimitotic drug on mechanical behaviours of the cytoskeleton in distinct grades of colon cancer cells. J. Biomech. 48:1172–1178, 2015.

    Article  PubMed  CAS  Google Scholar 

  32. 32.

    Sliogeryte, K., S. D. Thorpe, Z. Wang, C. L. Thompson, N. Gavara, and M. M. Knight. Differential effects of LifeAct-GFP and actin-GFP on cell mechanics assessed using micropipette aspiration. J. Biomech. 49:310–317, 2016.

    Article  PubMed  PubMed Central  Google Scholar 

  33. 33.

    Theret, D. P., M. J. Levesque, M. Sato, R. M. Nerem, and L. T. Wheeler. The application of a homogeneous half-space model in the analysis of endothelial cell micropipette measurements. ASME J. Biomech. Eng. 110:190–199, 1988.

    Article  CAS  Google Scholar 

  34. 34.

    Timoshenko, S. P., and J. N. Goodier. Theory of Elasticity (3rd edition). New York: McGraw-Hill Book Company, 1970.

    Google Scholar 

  35. 35.

    Vogel, V., and M. Sheetz. Local force and geometry sensing regulate cell functions. Nat. Rev. Mol. Cell Biol. 7:265–275, 2006.

    Article  PubMed  CAS  Google Scholar 

  36. 36.

    Wang, Z., A. K. T. Wann, C. L. Thompson, A. Hassen, W. Wang, and M. M. Knight. IFT88 influences chondrocyte actin organization and biomechanics. Osteoarthr. Cartil. 24:544–554, 2016.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  37. 37.

    Xie, J. J., W. J. Hu, and J. L. Tao. Quasi-static experimental study on the energy dissipation performance of foam rubber based on quasi static. China Meas. Test. Technol. 38:29–32, 2012; ((In Chinese)).

    CAS  Google Scholar 

  38. 38.

    Zhang, Q. Y. Mechanical properties of chondrocytes from normal and osteoarthritic rabbit knee cartilage. Dissertation for the Master Degree of Taiyuan University of Technology, 2006 (In Chinese)

  39. 39.

    Zhang, Q. Y., X. H. Wang, X. C. Wei, and W. Y. Chen. Characterization of viscoelastic properties of normal and osteoarthritic chondrocytes in experimental rabbit model. Osteoarthr. Cartil. 16:837–840, 2008.

    Article  PubMed  CAS  Google Scholar 

  40. 40.

    Zhou, E. H., C. T. Lim, and S. T. Quek. Finite element simulation of the micropipette aspiration of a living cell undergoing large viscoelastic deformation. Mech. Adv. Mater. Struct. 12:501–512, 2005.

    Article  Google Scholar 

Download references

Acknowledgments

Supports from the National Natural Science Foundation of China (Grant Nos. 11572213, 11632013, 11702184 and 11472185), the Natural Science Foundation of Shanxi Province, China (Grant No. 2014021013), and the Youth Funds of Taiyuan University of Technology (No. 2013T079) are acknowledged.

Conflict of interest

None of the authors have any competing financial interests related to this paper.

Author information

Affiliations

Authors

Corresponding author

Correspondence to WeiYi Chen.

Additional information

Associate Editor Sean S. Kohles oversaw the review of this article.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Chen, J., Wang, L. et al. Experimental Verification of the Elastic Formula for the Aspirated Length of a Single Cell Considering the Size and Compressibility of Cell During Micropipette Aspiration. Ann Biomed Eng 46, 1026–1037 (2018). https://doi.org/10.1007/s10439-018-2023-9

Download citation

Keywords

  • Cell mechanics
  • Micropipette aspiration
  • Cell model
  • Mechanical properties
  • Experimental verification