The micropipette aspiration test has been used extensively in recent years as a means of quantifying cellular mechanics and molecular interactions at the microscopic scale. However, previous studies have generally modeled the cell as an infinite half-space in order to develop an analytical solution for a viscoelastic solid cell. In this study, an axisymmetric boundary integral formulation of the governing equations of incompressible linear viscoelasticity is presented and used to simulate the micropipette aspiration contact problem. The cell is idealized as a homogenous and isotropic continuum with constitutive equation given by three-parameter $E,τ1,τ2$ standard linear viscoelasticity. The formulation is used to develop a computational model via a “correspondence principle” in which the solution is written as the sum of a homogeneous (elastic) part and a nonhomogeneous part, which depends only on past values of the solution. Via a time-marching scheme, the solution of the viscoelastic problem is obtained by employing an elastic boundary element method with modified boundary conditions. The accuracy and convergence of the time-marching scheme are verified using an analytical solution. An incremental reformulation of the scheme is presented to facilitate the simulation of micropipette aspiration, a nonlinear contact problem. In contrast to the halfspace model (Sato et al., 1990), this computational model accounts for nonlinearities in the cell response that result from a consideration of geometric factors including the finite cell dimension (radius R), curvature of the cell boundary, evolution of the cell–micropipette contact region, and curvature of the edges of the micropipette (inner radius a, edge curvature radius ε). Using 60 quadratic boundary elements, a micropipette aspiration creep test with ramp time $t*=0.1 s$ and ramp pressure $p*/E=0.8$ is simulated for the cases $a/R=0.3,$ 0.4, 0.5 using mean parameter values for primary chondrocytes. Comparisons to the half-space model indicate that the computational model predicts an aspiration length that is less stiff during the initial ramp response $t=0-1 s$ but more stiff at equilibrium $t=200 s.$ Overall, the ramp and equilibrium predictions of aspiration length by the computational model are fairly insensitive to aspect ratio $a/R$ but can differ from the half-space model by up to 20 percent. This computational approach may be readily extended to account for more complex geometries or inhomogeneities in cellular properties. [S0148-0731(00)00503-3]

1.
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
.
2.
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
.
3.
Maroudas, A., 1979, “Physicochemical Properties of Articular Cartilage,” in: Adult Articular Cartilage, M. Freeman, ed., Pitman Medical, Tunbridge Wells, pp. 215–290.
4.
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.
5.
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.
6.
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
.
7.
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
.
8.
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
157
.
9.
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
.
10.
Dong
,
C.
, and
Skalak
,
R.
,
1992
, “
Leukocyte Deformability: Finite Element Modeling of Large Viscoelastic Deformation
,”
J. Theor. Biol.
,
158
, pp.
173
193
.
11.
Evans
,
E.
, and
Yeung
,
A.
,
1989
, “
Apparent Viscosity and Cortical Tension of Blood Granulocytes Determined by Micropipette Aspiration
,”
Biophys. J.
,
56
, pp.
151
160
.
12.
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
269
.
13.
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
.
14.
Bagge
,
U.
,
Skalak
,
R.
, and
Attefors
,
R.
,
1977
, “
Granulocyte Rheology: Experimental Studies in an In Vitro Microflow System
,”
,
7
, pp.
29
48
.
15.
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
.
16.
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
.
17.
Shin
,
D.
, and
Athanasiou
,
K. A.
,
1997
, “
Biomechanical Properties of the Individual Cell
,”
Trans. Annu. Meet.—Orthop. Res. Soc.
,
22
, p.
352
352
.
18.
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
.
19.
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
.
20.
Guilak
,
F.
,
Tedrow
,
J. R.
, and
Burgkart
,
R.
,
2000
, “
Viscoelastic Properties of the Cell Nucleus
,”
Biochem. Biophys. Res. Commun.
,
269
, pp.
781
786
.
21.
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.
22.
Cruse
,
T. A.
,
Snow
,
D. W.
, and
Wilson
,
R. B.
,
1977
, “
Numerical Solutions in Axisymmetric Elasticity
,”
Comput. Struct.
,
7
, pp.
445
451
.
23.
Bakr, A. A., 1986, The Boundary Integral Equation Method in Axisymmetric Stress Analysis Problems, Springer-Verlag.
24.
Stroud, A. H., and Secrest, D., 1966, Gaussian Quadrature Formulas, Prentice-Hall, New York.