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TECHNICAL PAPERS

An Axisymmetric Boundary Integral Model for Assessing Elastic Cell Properties in the Micropipette Aspiration Contact Problem

[+] Author and Article Information
Mansoor A. Haider

Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695-8205  

Farshid Guilak

Orthopaedic Research Laboratories, 375 MSRB, Box 3093, Duke University Medical Center, Durham, NC 27710

J Biomech Eng 124(5), 586-595 (Sep 30, 2002) (10 pages) doi:10.1115/1.1504444 History: Received July 01, 1999; Revised May 01, 2002; Online September 30, 2002
Copyright © 2002 by ASME
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References

Frank,  E. H., and Grodzinsky,  A. J., 1987, “Cartilage Electromechanics-I. Electrokinetic Transduction and the Effects of Electrolyte pH and Ionic Strength,” J. Biomech., 20, pp. 615–627.
Guilak,  F., 1995, “Compression-induced Changes in the Shape and Volume of the Chondrocyte Nucleus,” J. Biomech., 28, pp. 1529–1542.
Maroudas, A., 1979, “Physicochemical Properties of Articular Cartilage,” In: Adult Articular Cartilage, edited by M. Freeman. Tunbridge Wells: Pitman Medical, pp. 215–290.
Mow, V. C., Bachrach, N., Setton, L. A., and Guilak, F., 1994, “Stress, Strain, Pressure, and Flow Fields in Articular Cartilage,” In: Cell Mechanics and Cellular Engineering, edited by V. C. Mow, F. Guilak, R. Tran-Son-Tay and R. Hochmuth. New York: Springer, Verlag, pp. 345–379.
Guilak, F., Sah, R. L., and Setton, L. A., 1997, “Physical Regulation of Cartilage Metabolism,” In: Basic Orthopaedic Biomechanics (2nd ed.), edited by V. C. Mow and W. C. Hayes. Philadelphia: Lippincott-Raven, pp. 179–207.
Guilak,  F., Jones,  W. R., Ting-Beall,  H. P., and Lee,  G. M., 1999a, “The Deformation Behavior and Mechanical Properties of Chondrocytes in Articular Cartilage,” Osteoarthritis Cartilage, 7, pp. 59–70.
Jones,  W. R., Ting-Beall,  H. P., Lee,  G. M., Kelley,  S. S., Hochmuth,  R. M., and Guilak,  F., 1999, “Alterations in Young’s Modulus and Volumetric Properties of Chondrocytes Isolated from Normal and Osteoarthritic Human Cartilage,” J. Biomech., 32, pp. 119–127.
Agresar,  G., Linderman,  J. J., Tryggvason,  G., and Powell,  K. G., 1998, “An Adaptive, Cartesian, Front-Tracking Method for the Motion, Deformation and Adhesion of Circulating Cells,” J. Comput. Phys., 143, pp. 346–380.
Dong,  C., and Skalak,  R., 1992, “Leukocyte Deformability: Finite Element Modeling of Large Viscoelastic Deformation,” J. Theor. Biol., 158, pp. 173–193.
Drury,  J. L., and Dembo,  M., 1999, “Hydrodynamics of Micropipette Aspiration,” Biophys. J., 76, pp. 110–128.
Evans,  E., and Yeung,  A., 1989, “Apparent Viscosity and Cortical Tension of Blood Granulocytes Determined by Micropipette Aspiration,” Biophys. J., 56, pp. 151–160.
Needham,  D., and Hochmuth,  R. M., 1990, “Rapid Flow of Passive Neutrophils into a 4 μm Pipet and Measurement of Cytoplasmic Viscosity,” J. Biomech., 112, pp. 269.
Tsai,  M. A., Frank,  R. S., and Waugh,  R. E., 1993, “Passive Mechanical—Behavior of Human Neutrophils—Power-Law Fluid,” Biophys. J., 65, pp. 2078–2088.
Bottino,  D. C., 1998, “Modeling Viscoelastic Networks and Cell Deformation in the Context of the Immersed Boundary Method,” J. Comput. Phys., 147, pp. 86–113.
Bagge,  U., Skalar,  R., and Attefors,  R., 1977, “Granulocyte Rheology: Experimental Studies in an In Vitro Microflow System,” Adv. Microcirc., 7, pp. 29–48.
Sato,  M., Theret,  D. P., Wheeler,  L. T., Ohshima,  N., and Nerem,  R. M., 1990, “Application of the Micropipette Technique to the Measurement of Cultured Porcine Aortic Endothelial Cell Viscoelastic Properties,” ASME J. Biomech. Eng., 112, pp. 263–268.
Schmid-Schonbein,  G. W., Sung,  K.-L. P., Tozeren,  H., Skalak,  R., and Chien,  S., 1981, “Passive Mechanical Properties of Human Leukocytes,” Biophys. J., 36, pp. 243–256.
Shin,  D., and Athanasiou,  K. A., 1999, “Cytoindentation for Obtaining Cell Biomechanical Properties,” J. Orthop. Res., 17, pp. 880–890.
Theret,  D. P., Levesque,  M. J., Sato,  M., Nerem,  R. M., and Wheeler,  L. T., 1988, “The Application of a Homogeneous Half-Space Model in the Analysis of Endothelial Cell Micropipette Measurements,” ASME J. Biomech. Eng., 110, pp. 190–199.
Guilak,  F., Ting-Beall,  H. P., Baer,  A. E., Jones,  W. R., Erickson,  G. R., and Setton,  L. A., 1999, “Viscoelastic Properties of Intervertebral Disc Cells: Identification of Two Biomechanically Distinct Populations,” Spine, 24, pp. 2475–2483.
Guilak,  F., and Ting-Beall,  H. P., 1999, “The Effects of Osmotic Presure on the Viscoelastic and Physical Properties of Articular Chondrocytes,” Adv. Bioeng., 43, pp. 103–104.
Lee,  D. A., Knight,  M. M., Bolton,  J. F., Idowu,  B. D., Kayser,  M. V., and Bader,  D. L., 2000, “Chondrocyte Deformation Within Compressed Agarose Constructs at the Cellular and Sub-cellular Levels,” J. Biomech., 33, pp. 81–95.
Guilak,  F., and Mow,  V. C., 2000, “The Mechanical Environment of the Chondrocyte: A Biphasic Finite Element Model of Cell-Matrix Interactions in Articular Cartilage,” J. Biomech., 33, pp. 1663–1673.
Cruse,  T. A., Snow,  D. W., and Wilson,  R. B., 1977, “Numerical Solutions in Axisymmetric Elasticity,” Comput. Struct., 7, pp. 445–451.
Rizzo,  F. J., 1967, “An Integral Equation Approach to Boundary Value Problems of Classical Elastostatics,” Q. Appl. Math., 25, pp. 83–95.
Bakr, A. A., 1986, The Boundary Integral Equation Method in Axisymmetric Stress Analysis Problems, Springer-Verlag.
Stroud, A. H., and Secrest, D., 1966, Gaussian Quadrature Formulae, Prentice-Hall, New York.
Abramowitz, M., and Stegun, I. A., 1972, Handbook of Mathematical Functions, Dover, New York.
Haider, M. A., and Guilak, F., 1999, “A Viscoelastic Boundary Element Model of Contact in the Micropipette Aspiration Test,” Proceedings of the Bioengineering Conference, ASME, 42 , pp. 339–340.
Haider,  M. A., and Guilak,  F., 2000, “An Axisymmetric Boundary Integral Model for Incompressible Linear Viscoelasticity: Application to the Micropipette Aspiration Contact Problem,” ASME J. Biomech. Eng., 122, pp. 236–244.

Figures

Grahic Jump Location
Adjustment factor for the Young’s modulus E, as predicted by the halfspace solution of Theret et al. 19, required to obtain agreement with predictions of the spherical cell model. The ratio of the wall function Φp≈2.1 and response function Ψ in equation (21) is plotted as a function of the aspiration length L/a for L/a>0.3 with scaled pressure increments of 0.01 until the characteristic strain exceeded a value of 0.2: (a) ε=0.02,M=50. (b) ε=0.05,M=40. (c) ε=0.08,M=40.
Grahic Jump Location
Video images of micropipette aspiration of a primary human chondrocyte: (a) Resting state of the cell with a tare pressure applied to form a seal between the cell and the micropipette. (b) As step pressures are applied, a portion of the cell enters the micropipette and the contact area between the cell and micropipette is gradually increased. (c) With larger pressures, the length of cell within the pipette may exceed the inner radius of the micropipette, and significant contact occurs between the cell and the inside wall of the micropipette (arrow). Scale bar equals 5 microns.
Grahic Jump Location
The cell response as measured by characteristic strain (L0−2R)/(2R) with increasing micropipette-to-cell aspect ratio a/R. The characteristic strain is shown as a function of the scaled pressure Δp/E for increments of 0.01 until the the value of the strain exceeded 0.2: (a) ε=0.02,M=50. (b) ε=0.05,M=40. (c) ε=0.08,M=40.
Grahic Jump Location
Sensitivity of the aspiration length L/a to the curvature ε/a of the micropipette edge for the case a/R=0.5. The aspiration length is shown as a function of the scaled pressure Δp/E for increments of 0.01 until the characteristic strain exceeded a value of 0.2.
Grahic Jump Location
The cell response as measured by the aspiration length L/a with increasing micropipette-to-cell aspect ratio a/R. The aspiration length is shown as a function of the scaled pressure Δp/E for increments of 0.01 until the characteristic strain exceeded a value of 0.2: (a) ε=0.02,M=50. (b) ε=0.05,M=40. (c) ε=0.08,M=40.
Grahic Jump Location
Simulations of the equilibrated elastic cell response using scaled pressure increments Δp/E=0.01 for the case ε/a=0.05,M=40. The deformed cell profiles are shown at equally spaced intervals of total applied pressure until the the characteristic strain exceeded a value of 0.2: (a) A small aspect ratio a/R=0.4. (b) A large aspect ratio a/R=0.7.
Grahic Jump Location
Computational mesh for the micropipette aspiration contact problem with M=40 quadratic boundary elements for the case a/R=0.4,ε/a=0.05: (a) Cell geometry and distribution of elements. The length L0 is used to compute a characteristic strain (L0−2R)/(2R) for the cell. (b) Micropipette geometry and illustration of cell-micropipette contact. The aspiration length L(p) is measured relative to the point with coordinates (0,0,R).

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