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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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.
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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.
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Creep response curves for the aspiration length L/a with varying aspect ratio a/R
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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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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.
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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.
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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.




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