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An Axisymmetric Boundary Integral Model for Incompressible Linear Viscoelasticity: Application to the Micropipette Aspiration Contact Problem

[+] Author and Article Information
Mansoor A. Haider

Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205e-mail: mahaider@math.ncsu.edu

Farshid Guilak

Orthopaedic Research Laboratories, 375 MSRB, Box 3093, Duke University Medical Center, Durham, NC 27710e -mail: guilak@duke.edu

J Biomech Eng 122(3), 236-244 (Feb 06, 2000) (9 pages) doi:10.1115/1.429654 History: Received December 27, 1999; Revised February 06, 2000
Copyright © 2000 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., Ratcliffe,  A., and Mow,  V. C., 1995, “Chondrocyte Deformation and Local Tissue Strain in Articular Cartilage: a Confocal Microscopy Study,” J. Orthop. Res., 13, pp. 410–421.
Maroudas, A., 1979, “Physicochemical Properties of Articular Cartilage,” in: Adult Articular Cartilage, M. Freeman, ed., Pitman Medical, Tunbridge Wells, 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, V. C. Mow, F. Guilak, R. Tran-Son-Tay, and R. Hochmuth, eds., Springer-Verlag, New York, pp. 345–379.
Guilak, F., Sah, R. L., and Setton, L. A., 1997, “Physical Regulation of Cartilage Metabolism,” in: Basic Orthopaedic Biomechanics, 2nd ed., V. C. Mow and W. C. Hayes, eds., Lippincott-Raven, Philadelphia, pp. 179–207.
Guilak,  F., Jones,  W. R., Ting-Beall,  H. P., and Lee,  G. M., 1999, “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.
Jones,  W. R., Lee,  G. M., Kelley,  S. S., and Guilak,  F., 1999, “Viscoelastic Properties of Chondrocytes From Normal and Osteoarthritic Human Cartilage,” Trans. Annu. Meet.—Orthop. Res. Soc., 24, p. 157.
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. Comp. Physiol., 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.
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,” ASME J. Biomech. Eng., 112, p. 269.
Bottino,  D. C., 1998, “Modeling Viscoelastic Networks and Cell Deformation in the Context of the Immersed Boundary Method,” J. Comp. Physiol., 147, pp. 86–113.
Bagge,  U., Skalak,  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 Leukocyctes,” Biophys. J., 36, pp. 243–256.
Shin,  D., and Athanasiou,  K. A., 1997, “Biomechanical Properties of the Individual Cell,” Trans. Annu. Meet.—Orthop. Res. Soc., 22, p. 352.
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., Trickey,  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., Tedrow,  J. R., and Burgkart,  R., 2000, “Viscoelastic Properties of the Cell Nucleus,” Biochem. Biophys. Res. Commun., 269, pp. 781–786.
Haider, M. A., and Guilak, F., 2000, “An Axisymmetric Boundary Integral Model for Assessing Elastic Cell Properties in the Micropipette Aspiration Contact Problem,” ASME J. Biomech. Eng., submitted.
Cruse,  T. A., Snow,  D. W., and Wilson,  R. B., 1977, “Numerical Solutions in Axisymmetric Elasticity,” Comput. Struct., 7, pp. 445–451.
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 Formulas, Prentice-Hall, New York.

Figures

Grahic Jump Location
Viscoelastic creep response of a chondrocyte to a step increase in pressure in the micropipette aspiration test. (a) A typical creep curve showing aspiration length of the cell into the micropipette versus time. The curve is characterized by an initial “jump” in displacement with application of the pressure, followed by an asymptotic creep until an equilibrium displacement is reached. This response is well-described by a three-parameter exponential curve-fit. (b) Video images of a primary human chondrocyte in the micropipette aspiration test. Images show the chondrocyte in the resting state under a tare pressure at time zero, followed by increasing cell displacement over time after step application of the test pressure.
Grahic Jump Location
A sample boundary element mesh for the micropipette aspiration contact problem with 40 quadratic boundary elements for the case a/R=0.4,ε/a=0.05. (a) Cell geometry and distribution of elements. (b) Micropipette geometry and illustration of cell-micropipette contact. The aspiration length L(t) is measured relative to the point with coordinates (0, 0, R) at t=0.
Grahic Jump Location
A simple axial compression. (a) The known traction components are prescribed on the boundary of a cylinder of unit radius. (b) The time-marching scheme is evaluated by comparing the axial displacement at (x1,x3)=(0,1) to the known solution (shown here) on the interval t=0–10 s.
Grahic Jump Location
Convergence of the time-marching scheme. The relative error is defined as the maximum value of the absolute difference between the computed and true solutions at (x1,x3)=(0,1) divided by the true solution at (x1,x3)=(0,1) on the interval t=0–10 s. This relative error is plotted with decreasing step-size.
Grahic Jump Location
Simulated cell response profiles in a micropipette aspiration creep test using 60 quadratic boundary elements with 4 quadrature points per element. The ramp response (t=0–0.1 s) is shown in gray at equal pressure increments and the creep response (t=0.1–200 s) is shown in black at equal time increments. Case a/R=0.3: (a) boundary element mesh at t=0, (b) deformed cell profiles. Case a/R=0.4: (c) boundary element mesh at t=0, (d) deformed cell profiles. Case a/R=0.5: (e) boundary element mesh at t=0, (f ) deformed cell profiles.
Grahic Jump Location
Creep response curves for the aspiration length L/a with varying aspect ratio a/R
Grahic Jump Location
Response curves for the aspiration length L/a compared to the viscoelastic half-space solution: (a) ramp response (t=0–0.1 s); (b) creep response (t=0.1–200 s)

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