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.
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November 1996
Technical Papers
A Three-Dimensional Finite Element Method for Large Elastic Deformations of Ventricular Myocardium: II—Prolate Spheroidal Coordinates
K. D. Costa,
K. D. Costa
Department of Bioengineering, University of California San Diego, La Jolla, CA
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P. J. Hunter,
P. J. Hunter
Department of Engineering Science, University of Auckland, Auckland, New Zealand
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J. S. Wayne,
J. S. Wayne
Department of Surgery, Virginia Commonwealth University, Richmond, VA
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L. K. Waldman,
L. K. Waldman
Department of Medicine, University of California San Diego, La Jolla, CA
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J. M. Guccione,
J. M. Guccione
Department of Mechanical Engineering, Washington University, St. Louis, MO
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A. D. McCulloch
A. D. McCulloch
Department of Bioengineering, University of California San Diego, La Jolla, CA
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K. D. Costa
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
A. D. McCulloch
Department of Bioengineering, University of California San Diego, La Jolla, CA
J Biomech Eng. Nov 1996, 118(4): 464-472 (9 pages)
Published Online: November 1, 1996
Article history
Received:
September 12, 1994
Revised:
October 10, 1995
Online:
October 30, 2007
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Citation
Costa, K. D., Hunter, P. J., Wayne, J. S., Waldman, L. K., Guccione, J. M., and McCulloch, A. D. (November 1, 1996). "A Three-Dimensional Finite Element Method for Large Elastic Deformations of Ventricular Myocardium: II—Prolate Spheroidal Coordinates." ASME. J Biomech Eng. November 1996; 118(4): 464–472. https://doi.org/10.1115/1.2796032
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