Material Properties and Residual Stress in the Stage 12 Chick Heart During Cardiac Looping

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

Department of Biomedical Engineering, Washington University, St. Louis, MO 63130

J Biomech Eng 126(6), 823-830 (Feb 04, 2005) (8 pages) doi:10.1115/1.1824129 History: Received January 08, 2004; Revised June 02, 2004; Online February 04, 2005
Copyright © 2004 by ASME
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Residual strain experiment. (a) Stage 12 chick embryo shown with intact heart. Cuts were made in outer curvature (OC) region of looping heart in either the (b) longitudinal or (c) circumferential direction (indicated by arrows). Details are given in text. (Figure reproduced from 8.)
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Finite element model for residual strain experiment. (a) Undeformed membrane representing myocardium is stretched equibiaxially by an amount λ. (b) Deformed membrane for λ=1.3. The cut, simulated by free nodes, opens. (Due to symmetry, only a quarter of the membrane is shown.) (c) Closeup of model in (b) showing stress distribution near the cut region. Note that the stresses decay rapidly with distance from the cut. (d) The geometric parameter α=R2/R1 for the cut is plotted as a function of the nondimensional material parameter BMY for several values of λ.
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Schematic of model geometry for indentation of embryonic heart. (a) The heart is a curved tube consisting of two primary structural layers, myocardium (MY) and cardiac jelly (CJ). Indentation is simulated by applying a force P to a rigid indenter. (b) To reduce computational costs for the FE model, the heart was treated as a flat circular plate (MY) with in-plane tension (arrows) on an elastic foundation (CJ) in the region near the indenter.
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Close-up near indenter of finite element model for indentation of cardiac jelly. Note the highly refined mesh near the indenter used to avoid excessive distortion of elements. The legend represents von Mises stress values and P is the indenter force.
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Video frames from a microindentation experiment on an intact heart showing the indenter tip. (a) Before contact with the heart; (b) immediately after contact; (c) during indentation. Arrows point to microspheres used to measure surface displacements (see text for details). Scale bar=100 μm. (Figure reproduced from 8.)
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Finite element 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, giving “intact” MY thickness h and radius R. (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 were recorded during the indentation.
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A set of parameter convergence curves for one representative indentation experiment. The value for κ=π/b (vertical dashes) was calculated by using the data for B̄ (see text for details).
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Force-displacement solution for CJ finite element indentation model with ACJ=3.0 Pa and BCJ=0.25 (solid line), along with all experimental curves for isolated CJ (dotted lines).
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Force-displacement (FD) (left column) and surface displacement data (right column) for several representative hearts. For the FD plots, the solid line represents the curve taken from the best-fit finite element solution, and the solid circles represent experimental data. In the contour plots, the solid lines represent surface displacement curves of increasing force (1–8 mdyn) for the best-fit solution and the open circles represent experimental bead displacements.
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Simulation of equibiaxial stretch test using simulated material parameters (solid curve), WGA solution (dotted curve), and best-fit finite element solution (dashed curve). The stress-stretch curve for the WGA solution lies closer to the test data than the best-fit solution.



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