On the Effects of Residual Stress in Microindentation Tests of Soft Tissue Structures

[+] Author and Article Information
Evan A. Zamir, Larry A. Taber

Department of Biomedical Engineering, Washington University, St. Louis, MO

J Biomech Eng 126(2), 276-283 (May 04, 2004) (8 pages) doi:10.1115/1.1695573 History: Received June 24, 2003; Revised November 03, 2003; Online May 04, 2004
Copyright © 2004 by ASME
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Schematics of (a) beam model and (b) plate model. Overbars are left out for notational convenience.
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Residual stress cutting experiment on stage 12 chick heart. (a) The c-shaped intact heart (H) is shown in the embryo. Cuts (b, c) are made in the myocardium at the outer curvature (OC) with a fine glass microneedle. (b) A heart is shown after a cut was made in the longitudinal direction (arrows). The elliptical wound opening is due to residual stress in the circumferential direction. (c) A cut in the circumferential direction (arrows) of a different heart gives a similar pattern of longitudinal opening.
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Nonlinear FE indentation model for embryonic heart: circular plate (myocardium, MY) on foundation (cardiac jelly, CJ). The analysis includes three steps (a-c): (a) MY thickness h0 and radius R0 are defined in the “zero-stress” state. (b) Radial stretch ratio λ is applied to the MY layer. (c) Indenter force P is then applied to the surface by a rigid indenter. (d) Close-up of mesh near the indenter shows the refinement of element size. The transverse displacements w of the MY surface nodes are recorded during the simulation.
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Schematic diagram of microindentation setup showing cross-section of embryonic heart. CCD=charge couple device (video camera), PZT=piezoelectric transducer, MY=myocardium,CJ=cardiac jelly.
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Video frames from an indentation experiment show the indenter tip. (a) Before contact with the heart; (b) immediately after contact; (c) during indentation. The arrows are pointing to 6-μm diameter microspheres that are used to measure tissue surface displacement. The dark ink spot on the tip is used to measure displacement of the tip. Scale bar=100 μm.
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Effects of flexural rigidity and foundation stiffness in linear models for beam (a) and plate (b). As D/K increases, the deformation becomes less localized. (Db/Kb=10n,n=1,2,3,4).
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Effects of in-plane load in linear models. Normalized displacement contours show that with increasing tension, the deflection becomes less localized for a beam (a) and more localized for a plate (b). Arrows points in direction of increasing tension for the beam (Tx=−50,0,100,1000) and the plate (Tr=−20,0,100,1000). Dashed lines indicate compressive loads. The ratio D/K=1000 was held fixed for all solutions. (c) For both models, the apparent stiffness k increases with increasing levels of tension.
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Equivalent stiffness contours for (a) beam and (b) plate models. In (c) and (d) the corresponding linear FD curves are given. The sets of parameters giving equivalent stiffness are listed in the figure legends.
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Effect of material and geometric nonlinearity on the normalized displacement contour Γ=w/w0 in FE model. The deformation spreads out from the indenter as force increases.
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(a) Experimental FD relation (circles) for a stage 12 chick heart is fit by models with residual stress (solid curve) or without residual stress (dashed curve). (b) Experimentally measured displacement contours (solid circles) are poorly fit with FE model (dashed curves) that does not include residual stress. (Contours are shown for indenter force P=2,4,6,8 mdynes.) (c) When residual stress is included in the model (λ=1.4), better fitting of the contours is possible, and the elastic modulus A decreases significantly (from 70 Pa to 3 Pa).




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