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TECHNICAL PAPERS: Soft Tissue

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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References

Domke,  J., Parak,  W. J., George,  M., Gaub,  H. E., and Radmacher,  M., 1999, “Mapping the mechanical pulse of single cardiomyocytes with the atomic force microscope,” Eur. Biophys. J., 28, pp. 179–186.
Sato,  M., Nagayama,  K., Kataoka,  N., Sasaki,  M., and Hane,  K., 2000, “Local mechanical properties measured by atomic force microscopy for cultured bovine endothelial cells exposed to shear stress,” J. Biomech., 33, pp. 127–135.
Rotsch,  C., and Radmacher,  M., 2000, “Drug-induced changes of cytoskeletal structure and mechanics in fibroblasts: an atomic force microscopy study,” Biophys. J., 78, pp. 520–535.
Mathur,  A. B., Collinsworth,  A. M., Reichert,  W. M., Kraus,  W. E., and Truskey,  G. A., 2001, “Endothelial, cardiac muscle and skeletal muscle exhibit different viscous and elastic properties as determined by atomic force microscopy,” Biophys. J., 34, pp. 1545–1553.
Bhadriraju,  K., and Hansen,  L. K., 2002, “Extracellular matrix-and cytoskeleton-dependent changes in cell shape and stiffness,” Exp. Cell Res., 278, pp. 92–100.
Matzke,  R., Jacobson,  K., and Radmacher,  M., 2001, “Direct, high-resolution measurement of furrow stiffening during division of adherent cells,” Nat. Cell Biol., 3, pp. 607–610.
Rotsch,  C., Jacobson,  K., and Radmacher,  M., 1999, “Dimensional and mechanical dynamics of active and stable edges in motile fibroblasts investigated by using atomic force microscopy,” Proc. Natl. Acad. Sci. U.S.A., 96, pp. 921–926.
Haider,  M. A., and Holmes,  M. H., 1997, “A mathematical approximation for the solution of a static indentation test,” J. Biomech., 30, pp. 747–751.
Sakamoto,  M., Li,  G., Hara,  T., and Chao,  E. Y., 1996, “A new method for theoretical analysis of static indentation test,” J. Biomech., 29, pp. 679–685.
Costa,  K. D., and Yin,  F. C., 1999, “Analysis of indentation: implications for measuring mechanical properties with atomic force microscopy,” J. Biomech. Eng., 121, pp. 462–471.
Humphrey,  J. D., Halperin,  H. R., and Yin,  F. C. P., 1991, “Small Indentation Superimposed on a Finite Equibiaxial Stretch: Implications for Cardiac Mechanics,” J. Appl. Mech., 58, pp. 1108–1111.
Kiehart,  D. P., Galbraith,  C. G., Edwards,  K. A., Rickoll,  W. L., and Montague,  R. A., 2000, “Multiple forces contribute to cell sheet morphogenesis for dorsal closure in Drosophila,” J. Cell Biol., 149, pp. 471–490.
Donnell, L. H., 1976, Beams, Plates, and Shells, McGraw-Hill, New York.
Szilard, R., 1974, Theory and Analysis of Plates, Prentice-Hall, Englewood Cliffs, NJ.
Shampine, Lawrence F., Kierzenka, Jacek, and Reichelt, Mark W., “Solving Boundary Value Problems for Ordinary Differential Equations in MATLAB with bvp4c,” 10-26-2000, ftp://ftp.mathworks.com/pub/doc/papers/bvp/.
M. Hetenyi, 1946, Beams on Elastic Foundation, The University of Michigan Press, Ann Arbor.
Timoshenko, S. and Woinowsky-Krieger, S., 1959, Theory of Plates and Shells, McGraw-Hill Book Company, Inc., New York.
Manner,  J., 2000, “Cardiac Looping in the Chick Embryo: A Morphological Review with Special Reference to Terminological and Biomechanical Aspects of the Looping Process,” Anat. Rec., 259, pp. 248–262.
Taber,  L. A., Hu,  N., Pexieder,  T., Clark,  E. B., and Keller,  B. B., 1993, “Residual Strain in the Ventricle of the Stage 16--24 Chick Embryo,” Circ. Res., 72, pp. 455–462.
Karduna,  A. R., Halperin,  H. R., and Yin,  F. C., 1997, “Experimental and numerical analyses of indentation in finite-sized isotropic and anisotropic rubber-like materials,” Ann. Biomed. Eng., 25, pp. 1009–1016.
Zamir, EA, Srinivasan, V, Perucchio, R., and Taber, LA, Mechanical Asymmetry in the Embryonic Chick Heart During Looping, Annals of Biomedical Engineering 31 , pp. 1327–1336.
Hamburger,  V., and Hamilton,  H. L., 1951, “A Series of Normal Stages in the Development of the Chick Embryo,” J. Morphol., 88, pp. 49–92.
Voronov,  D. A., and Taber,  L. A., 2002, “Cardiac looping in experimental conditions: Effects of extraembryonic forces,” Dev. Dyn., 224, pp. 413–421.
Nakamura,  A., and Manasek,  F. J., 1978, “Experimental Studies of the Shape and Structure of Isolated Cardiac Jelly,” J. Embryol. Exp. Morphol., 43, pp. 167–183.
Daily,  B., Elson,  E. L., and Zahalak,  G. I., 1984, “Cell poking. Determination of the elastic area compressibility modulus of the erythrocyte membrane,” Biophys. J., 45, pp. 671–682.
Fung,  Y. C., and Liu,  S. Q., 1992, “Strain Distribution in Small Blood Vessels with Zero-Stress State Taken into Consideration,” Am. J. Physiol., 262, pp. H544–H552.
Liu,  S. Q., and Fung,  Y. C., 1998, “Zero-Stress States of Arteries,” J. Biomech. Eng., 110, pp. 82–84.
Omens,  J. H., and Fung,  Y. C., 1990, “Residual Strain in Rat Left Ventricle,” Circ. Res., 66, pp. 37–45.
Hofmann,  U. G., Rotsch,  C., Parak,  W. J., and Radmacher,  M., 1997, “Investigating the Cytoskeleton of Chicken Cardiocytes with the Atomic Force Microscope,” J. Struct. Biol., 119, pp. 84–91.
Radmacher,  M. 1997, “Measuring the Elastic Properties of Biological Samples with the AFM,” IEEE Eng. Med. Biol. Mag., 16, pp. 47–57.
Sato,  M., Nagayama,  K., Kataoka,  N., Sasaki,  M., and Hane,  K., 2000, “Local mechanical properties measured by atomic force microscopy for cultured bovine endothelial cells exposed to shear stress,” J. Biomech., 33, pp. 127–135.
Halperin,  H. R., Chew,  P. H., Weisfeldt,  M. L., Sagawa,  K., Humphrey,  J. D., and Yin,  F. C. P., 1987, “Transverse Stiffness: A Method for Estimation of Myocardial Wall Stress,” Circ. Res., 61, pp. 695–703.
Ulfendahl,  M., Chan,  E., McConnaughey,  W. B., Prost-Domasky,  S., and Elson,  E. L., 1998, “Axial and Transverse Stiffness Measures of Cochlear Outer Hair Cells Suggest a Common Mechanical Basis,” Pflugers Archive, 436, pp. 9–15.
Hale,  J. E., Rudert,  M. J., and Brown,  T. D., 1993, “Indentation assessment of biphasic mechanical property deficits in size-dependent osteochondral defect repair,” J. Biomech., 26, pp. 1319–1325.
Hayes,  W. C., Keer,  L. M., Herrmann,  G., and Mockros,  L. F., 1972, “A mathematical analysis for indentation tests of articular cartilage,” J. Biomech., 5, pp. 541–551.
Hori,  R. Y., and Mockros,  L. F., 1976, “Indentation tests of human articular cartilage,” J. Biomech., 9, pp. 259–268.
Jurvelin,  J., Kiviranta,  I., Saamanen,  A. M., Tammi,  M., and Helminen,  H. J., 1990, “Indentation stiffness of young canine knee articular cartilage—influence of strenuous joint loading,” J. Biomech., 23, pp. 1239–1246.
Kempson,  G. E., Freeman,  M. A., and Swanson,  S. A., 1971, “The determination of a creep modulus for articular cartilage from indentation tests of the human femoral head,” J. Biomech., 4, pp. 239–250.
Suh,  J. K., and Spilker,  R. L., 1994, “Indentation analysis of biphasic articular cartilage: nonlinear phenomena under finite deformation,” J. Biomech. Eng., 116, pp. 1–9.
Itasaki,  N., Nakamura,  H., and Yasuda,  M., 1989, “Changes in the Arrangement of Actin Bundles During Heart Looping in the Chick Embryo,” Anat. Embryol. (Berl), 180, pp. 413–420.
Costa,  K. D., May-Newman,  K., Farr,  D., O’Dell,  W. G., McCulloch,  A. D., and Omens,  J. H., 1997, “Three-dimensional Residual Strain in Midanterior Canine Left Ventricle,” Am. J. Physiol., 273, pp. H1968–H1976.
Fung,  Y. C., and Liu,  S. Q., 1989, “Change of Residual Strains in Arteries due to Hypertrophy Caused by Aortic Constriction,” Circ. Res., 65, pp. 1340–1349.
Han,  H. C., and Fung,  Y. C., 1991, “Residual Strains in Porcine and Canine Trachea,” J. Biomech., 24, pp. 307–315.
Charras,  G. T., and Horton,  M. A., 2002, “Determination of cellular strains by combined atomic force microscopy and finite element modeling,” Biophys. J., 83, pp. 858-879.
Charras,  G. T., and Horton,  M. A., 2002, “Single cell mechanotransduction and its modulation analyzed by atomic force microscope indentation,” Biophys. J., 82, pp. 2970–2981.

Figures

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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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