Technical Briefs

Viscoelastic Material Properties of the Myocardium and Cardiac Jelly in the Looping Chick Heart

[+] Author and Article Information
Jiang Yao1 n2

 Department of Mechanical Engineering,University of Rochester, Rochester, NY, 14627jiang.yao@3ds.com

Victor D. Varner

 Department of Biomedical Engineering,Washington University, St. Louis, MO 63130vdv1@cec.wustl.edu

Lauren L. Brilli3

 Department of Developmental Biology,University of Pittsburgh, Pittsburgh, PA, 15261brilli.lauren@medstudent.pitt.edu

Jonathan M. Young4

 Department of Mechanical Engineering,University of Rochester, Rochester, NY, 14627jyoung@bm.technion.ac.il

Larry A. Taber

 Department of Biomedical Engineering,Washington University, St. Louis, MO 63130lat@wustl.edu

Renato Perucchio

 Department of Mechanical Engineering,University of Rochester, Rochester, NY, 14627rlp@me.rochester.edu


Corresponding author.


Present address: Dassault Systemes Simulia Corp., 166 Valley Street, Providence, RI, 02902-2499.


Present address: Department of Development Biology, University of Pittsburgh.


Present address: Faculty of Biomedical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel.

J Biomech Eng 134(2), 024502 (Feb 15, 2012) (7 pages) doi:10.1115/1.4005693 History: Received November 29, 2011; Revised December 01, 2011; Posted January 24, 2012; Published February 14, 2012; Online February 15, 2012

Accurate material properties of developing embryonic tissues are a crucial factor in studies of the mechanics of morphogenesis. In the present work, we characterize the viscoelastic material properties of the looping heart tube in the chick embryo through nonlinear finite element modeling and microindentation experiments. Both hysteresis and ramp-hold experiments were performed on the intact heart and isolated cardiac jelly (extracellular matrix). An inverse computational method was used to determine the constitutive relations for the myocardium and cardiac jelly. With both layers assumed to be quasilinear viscoelastic, material coefficients for an Ogden type strain-energy density function combined with Prony series of two terms or less were determined by fitting numerical results from a simplified model of a heart segment to experimental data. The experimental and modeling techniques can be applied generally for determining viscoelastic material properties of embryonic tissues.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

(a) Schematic of heart cross section showing indentation of the side of the heart (MY: myocardium; CJ: cardiac jelly; EN: endocardium; L: lumen). (b) Axisymmetric cylindrical model with 8-node quadratic hybrid elements was used to represent the indentation experiment. Roller boundary conditions were specified along the bottom edge of the CJ, and the outer boundary was free. The mesh was refined near the indenter, and the mesh density was determined by a convergence test. The residual stress in MY was modeled as a radial stretch applied to the MY layer. During the initial stretch, interaction between the MY and CJ was frictionless. Then, the MY was tied to the CJ so that there was no relative motion between the two layers during indentation. The contact between the indenter and the heart was modeled as frictionless hard contact with no penetration allowed between the contacting surfaces.

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Figure 2

Experimentally measured displacement-time data were prescribed as displacement history of the rigid indenter in the finite element models of (a) hysteresis and (c) ramp-hold tests. Viscoelastic material properties of the indented tissue were inversely computed by fitting the FE predictions (solid line) in force-time responses to experimental measurements from (b) hysteresis and (d) ramp-hold tests.

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Figure 3

(a) Force-displacement curves of hysteresis test and (b) force-time curves of ramp-hold test for one representative CJ isolate (No. 3 in Table 1). Viscoelastic FE models (solid lines) generally agree with experimental measurements (circles).

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Figure 4

(a) Force-displacement curves of hysteresis tests with two representative loading/unloading rates for one representative intact heart (No. 1 in Table 2). (b) Force-time curves of ramp-hold tests with two indentation depths for another representative intact heart (No. 11 in Table 2). Best-fit viscoelastic finite element solutions (solid lines) using Ogden strain energy density function are shown together with experimental data (circles and squares).

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Figure 5

Mean relaxation functions versus time for CJ (both exponential and Ogden strain energy density functions) and MY in (a) full view and (b) zoomed view. These relaxation functions were plotted using the mean Prony series parameters in Tables  12.

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Figure 6

Force-displacement curves of hysteresis tests with (a and b) two representative loading/unloading rates and (c) force-time curve of ramp-hold test for the MY average experimental data (dotted lines). The solid lines represent the best-fit curves when the objective is to fit one hysteresis rate and ramp-hold curve only; the dash lines represent the best-fit curves when the object is to fit two hysteresis curves only; the dashed-dotted lines represent the best-fit curves when the object is to fit ramp-hold curve only.



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