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Research Papers

Compressibility and Anisotropy of the Ventricular Myocardium: Experimental Analysis and Microstructural Modeling

[+] Author and Article Information
Eoin McEvoy

Department of Biomedical Engineering,
National University of Ireland Galway,
Galway H91 TK33, Ireland
e-mail: e.mcevoy5@nuigalway.ie

Gerhard A. Holzapfel

Institute of Biomechanics,
Graz University of Technology,
Graz 8010, Austria;
Faculty of Engineering Science and Technology,
Norwegian University of Science and
Technology (NTNU),
Trondheim 7491, Norway
e-mail: holzapfel@TUGraz.at

Patrick McGarry

Department of Biomedical Engineering,
National University of Ireland Galway,
Galway H91 TK33, Ireland
e-mail: Patrick.mcgarry@nuigalway.ie

1Corresponding author.

Manuscript received December 15, 2017; final manuscript received April 2, 2018; published online May 24, 2018. Assoc. Editor: Rouzbeh Amini.

J Biomech Eng 140(8), 081004 (May 24, 2018) (10 pages) Paper No: BIO-17-1590; doi: 10.1115/1.4039947 History: Received December 15, 2017; Revised April 02, 2018

While the anisotropic behavior of the complex composite myocardial tissue has been well characterized in recent years, the compressibility of the tissue has not been rigorously investigated to date. In the first part of this study, we present experimental evidence that passive-excised porcine myocardium exhibits volume change. Under tensile loading of a cylindrical specimen, a volume change of 4.1±1.95% is observed at a peak stretch of 1.3. Confined compression experiments also demonstrate significant volume change in the tissue (loading applied up to a volumetric strain of 10%). In order to simulate the multiaxial passive behavior of the myocardium, a nonlinear volumetric hyperelastic component is combined with the well-established Holzapfel–Ogden anisotropic hyperelastic component for myocardium fibers. This framework is shown to describe the experimentally observed behavior of porcine and human tissues under shear and biaxial loading conditions. In the second part of the study, a representative volumetric element (RVE) of myocardium tissue is constructed to parse the contribution of the tissue vasculature to observed volume change under confined compression loading. Simulations of the myocardium microstructure suggest that the vasculature cannot fully account for the experimentally measured volume change. Additionally, the RVE is subjected to six modes of shear loading to investigate the influence of microscale fiber alignment and dispersion on tissue-scale mechanical behavior.

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Figures

Grahic Jump Location
Fig. 2

(a) Experimental (mean ± standard error of the mean (sem)) and simulated nominal stress (kPa) during stretch of the myocardium specimens, (b) experimental (mean ± sem) and simulated volume change (%) during stretch, and (c) experimental (mean ± sem) and simulated nominal stress (kPa) during confined compression

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Fig. 1

Overview of the compressibility study: (a) specimen preparation from a porcine heart; (b) sample is stretched between two platens and the volume change is determined; (c) confined compression tests are performed to support the analysis; and (d) flowchart outlining the inverse finite element (FE) scheme is implemented to calibrate material parameters for the constitutive modeling. The experimental and simulated volume change ΔV/V0 and force T are compared.

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Fig. 3

Experimental and simulated shear behavior for (a) porcine [3] and (b) human myocardium [4]; (c) maximum principal strain in a simulated biaxial sample; (d) experimental and simulated biaxial behavior for human myocardium [4], with stretch in the MFD and cross-fiber (CFD) directions.

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Fig. 4

Representative volumetric element of the myocardium with discrete regions for the cardiomyocytes, the matrix surrounding the cells (ECM 1), and the matrix surrounding the myocardial sheets (ECM 2). Capillaries are included as empty vessels.

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Fig. 5

Discrete model (solid curve) and GST model (circles) for three cases of dispersion: case 1 (slight dispersion) with b = 10, d=0.02; case 2 (intermediate dispersion) with b = 1.5, d=0.14; case 3 (near isotropic dispersion) with b = 0.1, d=0.24. The shear stress is normalized by the isotropic shear modulus μ, according to τ/μ.

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Fig. 6

Maximum principal strain following loading of the RVE: (a) confined compression, cc; (b) shear in the ns plane; and (c) shear in the sn plane

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Fig. 7

(a) Experimental and simulated (from RVE) stress for confined compression; (b) volume decrease of each region following compression (i.e., the vasculature, cells, ECM1, and ECM2); and (c) proportion that the vascular and solid components account for the total volume change

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Fig. 8

Simulated shear stress from RVE analyses of (a) porcine and (b) human tissue. Experimental data from (a) Dokos et al. [3] and (b) Sommer et al. [4] superimposed for reference.

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Fig. 9

(a) Cross section taken at midplane of simulated tensile experiment to measure ellipticity; (b) experimental and simulated ellipticity with porcine and human material parameters; (c) simulated nominal stress (kPa) versus volumetric strain for a simulated micromodel confined compression in f, s, and n directions; and (d) simulated nominal stress (kPa) versus stretch for the micromodel under tensile loading

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