A Three-Dimensional Finite Element Method for Large Elastic Deformations of Ventricular Myocardium: I—Cylindrical and Spherical Polar Coordinates

[+] Author and Article Information
K. D. Costa, A. D. McCulloch

Department of Bioengineering, University of California San Diego, La Jolla, CA

P. J. Hunter

Department of Engineering Science, University of Auckland, Auckland, New Zealand

J. M. Rogers

Department of Medicine, University of Alabama at Birmingham, Birmingham, AL

J. M. Guccione

Department of Mechanical Engineering, Washington University, St. Louis, MI

L. K. Waldman

Department of Medicine, University of California San Diego, La Jolla, CA

J Biomech Eng 118(4), 452-463 (Nov 01, 1996) (12 pages) doi:10.1115/1.2796031 History: Received September 12, 1994; Revised October 10, 1995; Online October 30, 2007


A three-dimensional Galerkin finite element method was developed for large deformations of ventricular myocardium and other incompressible, nonlinear elastic, anisotropic materials. Cylindrical and spherical elements were used to solve axisymmetric problems with r.m.s. errors typically less than 2 percent. Isochoric interpolation and pressure boundary constraint equations enhanced low-order curvilinear elements under special circumstances (69 percent savings in degrees of freedom, 78 percent savings in solution time for inflation of a thick-walled cylinder). Generalized tensor products of linear Lagrange and cubic Hermite polynomials permitted custom elements with improved performance, including 52 percent savings in degrees of freedom and 66 percent savings in solution time for compression of a circular disk. Such computational efficiencies become significant for large scale problems such as modeling the heart.

Copyright © 1996 by The American Society of Mechanical Engineers
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