A Three-Dimensional Finite Element Method for Large Elastic Deformations of Ventricular Myocardium: II—Prolate Spheroidal 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. S. Wayne

Department of Surgery, Virginia Commonwealth University, Richmond, VA

L. K. Waldman

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

J. M. Guccione

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

J Biomech Eng 118(4), 464-472 (Nov 01, 1996) (9 pages) doi:10.1115/1.2796032 History: Received September 12, 1994; Revised October 10, 1995; Online October 30, 2007


A three-dimensional finite element method for nonlinear finite elasticity is presented using prolate spheroidal coordinates. For a thick-walled ellipsoidal model of passive anisotropic left ventricle, a high-order (cubic Hermite) mesh with 3 elements gave accurate continuous stresses and strains, with a 69 percent savings in degrees of freedom (dof) versus a 70-element standard low-order model. A custom mixed-order model offered 55 percent savings in dof and 39 percent savings in solution time compared with the low-order model. A nonsymmetric 3D model of the passive canine LV was solved using 16 high-order elements. Continuous nonhomogeneous stresses and strains were obtained within 1 hour on a laboratory workstation, with an estimated solution time of less than 4 hours to model end-systole. This method represents the first practical opportunity to solve large-scale anatomically detailed models for cardiac stress analysis.

Copyright © 1996 by The American Society of Mechanical Engineers
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