Cytoindentation Theory and Experiment for Obtaining Cell Biomechanical Properties

A novel mechanical testing methodology has been developed for obtaining the intrinsic material properties of the individual cell attached on a rigid substrate. Displacement-controlled indentation tests were conducted on the surface of individual cells and the corresponding surface reaction force offered by each cell was measured using a newly designed cell indentation apparatus (cytoindenter). The cytoindenter consists of a piezoelectric translator for driving the indenting probe (5 um dia.), a dual photodiode for position detection, and a closed-loop computer system for commanding the piezoelectric translator and for acquiring the displacement data. Precise position detection of the indenting probe is achieved by projecting the image of a carbon filament (7 um dia.), which is attached to the indenting probe, onto the plane where the photodiode is positioned. Force measurement uses a glass cantilever beam (75 μm dia.), which is deflected by the rigidity of the cell being indented. The cytoindenter developed in this study is sensitive enough to measure forces to the order of a nanonewton (1x10^-9 N).

Cells were modeled using the linear biphasic theory under the assumption that each cell's viscoelastic behavior is due to the interaction between the solid cytoskeletal matrix and the cytoplasmic fluid. To obtain the intrinsic material properties (aggregate modulus-H_A, Poisson's ratio-ν, and permeability-k), the experimental surface reaction force vs. deformation data were curvefitted with predicted solutions obtained from using the linear biphasic finite element code in conjunction with optimization routines.

The results indicated that the MG63 osteoblast-like cell has a compressive modulus of 2.05 +0.89 (KPa) which is 2-3 orders of magnitude smaller than that of articular cartilage, 4-5 orders of magnitude smaller than that of compact bone, and quite similar to that of leukocytes. The permeability is 1.18+0.65 (x10^-10 m⁴/Ns) which is 4-6 orders of magnitude larger than that of cartilage. The Poisson's ratio of MG63 cells is 0.37+0.03. The intrinsic material properties of the individual cell found in this study can be useful in quantifying precise mechanical stimuli acting on cells. This information is also needed for theories attempting to establish mechanotransductional relationships. viii

Year	Entry
1986	Mak AF. The apparent viscoelastic behavior of articular cartilage: the contributions from the intrinsic matrix viscoelasticity and interstitial fluid flows. J Biomech Eng. May 1986;108(2):123-130.
1987	Mak AF, Lai WM, Mow VC. Biphasic indentation of articular cartilage, I: theoretical analysis. J Biomech. 1987;20(7):703-714.
1972	Hayes WC, Keer LM, Herrmann G, Mockros LF. A mathematical analysis for indentation tests of articular cartilage. J Biomech. September 1972;5(5):541-551.
1993	Giori NJ, Beaupré GS, Carter DR. Cellular shape and pressure may mediate mechanical control of tissue composition in tendons. J Orthop Res. July 1993;11(4):581-591.
1994	Mow VC, Bachrach NM, Setton LA, Guilak F. Stress, strain, pressure and flow fields in articular cartilage and chondrocytes. In: Mow VC, Tran-Son-Tay R, Guilak F, Hochmuth RM, eds. Cell Mechanics and Cellular Engineering. Symposium on Cell Mechanics and Cellular Engineering; July 10-15, 1994. New York, NY: Springer-Verlag; 1994:345-379.
1992	Spilker RL, Donzelli PS, Mow VC. A transversely isotropic biphasic finite element model of the meniscus. J Biomech. September 1992;25(9):1027-1045.
1992	Spilker RL, Suh J-K, Mow VC. A finite element analysis of the indentation stress-relaxation response of linear biphasic articular cartilage. J Biomech Eng. May 1992;114(2):191-201.
1990	Spilker RL, Suh J-K, Mow VC. Effects of friction on the unconfined compressive response of articular cartilage: a finite element analysis. J Biomech Eng. May 1990;112(2):138-146.
1993	Setton LA, Zhu W, Weidenbaum M, Ratcliffe A, Mow VC. Compressive properties of the cartilaginous end-plate of the baboon lumbar spine. J Orthop Res. March 1993;11(2):228-239.
1988	Carter DR, Wong M. Mechanical stresses and endochondral ossification in the chondroepiphysis. J Orthop Res. January 1988;6(1):148-154.
1994	Freeman PM, Natarajan RN, Kimura JH, Andriacchi TP. Chondrocyte cells respond mechanically to compressive loads. J Orthop Res. May 1994;12(3):311-320.
1994	Guilak F, Donahue HJ, Zell RA, Grande D, McLeod KJ, Rubin CT. Deformation-induced calcium signaling in articular chondrocytes. In: Mow VC, Tran-Son-Tay R, Guilak F, Hochmuth RM, eds. Cell Mechanics and Cellular Engineering. Symposium on Cell Mechanics and Cellular Engineering; July 10-15, 1994. New York, NY: Springer-Verlag; 1994:380-397.
1965	Sneddon IN. The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int J Eng Sci. May 1965;3(1):47-57.
1981	Roesler H. Some historical remarks on the theory of cancellous bone structure (Wolff's Law). In: Cowin SC, ed. Mechanical Properties of Bone. The Joint ASME-ASCE Applied Mechnics, Fluids Engineering and Bioengineering Conference; June 22-24, 1981; Boulder, CO. New York, NY: American Society of Mechical Engineers; 1981:27-42.
1989	Mow VC, Gibbs MC, Lai WM, Zhu WB, Athanasiou KA. Biphasic indentation of articular cartilage, II: a numerical algorithm and an experimental study. J Biomech. 1989;22:853-861.
1980	Mow VC, Kuei SC, Lai WM, Armstrong CG. Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments. J Biomech Eng. February 1980;102(1):73-84.
1986	Wolff J. The Law of Bone Remodelling. Maquet P, Furlong R, trans. New York, NY: Springer; 1986.
1994	Athanasiou KA, Agarwal A, Dzida FJ. Comparative study of the intrinsic mechanical properties of the human acetabular and femoral head cartilage. J Orthop Res. May 1994;12(3):340-349.
1995	Athanasiou KA, Agarwal A, Muffoletto A, Dzida FJ, Constantinides G, Clem M. Biomechanical properties of hip cartilage in experimental animal models. Clin Orthop Relat Res. July 1995;316:254-266.
1991	Athanasiou KA, Rosenwasser MP, Buckwalter JA, Malinin TI, Mow VC. Interspecies comparisons of in situ intrinsic mechanical properties of distal femoral cartilage. J Orthop Res. May 1991;9(3):330-340.
1995	Athanasiou KA, Niederauer GG, Schenck RC Jr. Biomechanical topography of human ankle cartilage. Ann Biomed Eng. September–October 1995;23(5):697-704.

Year

Entry

1986

Mak AF. The apparent viscoelastic behavior of articular cartilage: the contributions from the intrinsic matrix viscoelasticity and interstitial fluid flows. J Biomech Eng. May 1986;108(2):123-130.

1987

Mak AF, Lai WM, Mow VC. Biphasic indentation of articular cartilage, I: theoretical analysis. J Biomech. 1987;20(7):703-714.

1972

Hayes WC, Keer LM, Herrmann G, Mockros LF. A mathematical analysis for indentation tests of articular cartilage. J Biomech. September 1972;5(5):541-551.

1993

Giori NJ, Beaupré GS, Carter DR. Cellular shape and pressure may mediate mechanical control of tissue composition in tendons. J Orthop Res. July 1993;11(4):581-591.

1994

Mow VC, Bachrach NM, Setton LA, Guilak F. Stress, strain, pressure and flow fields in articular cartilage and chondrocytes. In: Mow VC, Tran-Son-Tay R, Guilak F, Hochmuth RM, eds. Cell Mechanics and Cellular Engineering. Symposium on Cell Mechanics and Cellular Engineering; July 10-15, 1994. New York, NY: Springer-Verlag; 1994:345-379.