Insights into the passive mechanical behavior of left ventricular myocardium using a robust constitutive model based on full 3D kinematics

David S. Li, Reza Avazmohammadi, Samer S. Merchant, Tomonori Kawamura, Edward W. Hsu, Joseph H. Gorman, Robert C. Gorman, Michael S. Sacks

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


Myocardium possesses a hierarchical structure that results in complex three-dimensional (3D) mechanical behavior, forming a critical component of ventricular function in health and disease. A wide range of constitutive model forms have been proposed for myocardium since the first planar biaxial studies were performed by Demer and Yin (J. Physiol. 339 (1), 1983). While there have been extensive studies since, none have been based on full 3D kinematic data, nor have they utilized optimal experimental design to estimate constitutive parameters, which may limit their predictive capability. Herein we have applied our novel 3D numerical-experimental methodology (Avazmohammadi et al., Biomechanics Model. Mechanobiol. 2018) to explore the applicability of an orthotropic constitutive model for passive ventricular myocardium (Holzapfel and Ogden, Philos. Trans. R. Soc. Lond.: Math. Phys. Eng. Sci. 367, 2009) by integrating 3D optimal loading paths, spatially varying material structure, and inverse modeling techniques. Our findings indicated that the initial model form was not successful in reproducing all optimal loading paths, due to previously unreported coupling behaviors via shearing of myofibers and extracellular collagen fibers in the myocardium. This observation necessitated extension of the constitutive model by adding two additional terms based on the I8(C) pseudo-invariant in the fiber-normal and sheet-normal directions. The modified model accurately reproduced all optimal loading paths and exhibited improved predictive capabilities. These unique results suggest that more complete constitutive models are required to fully capture the full 3D biomechanical response of left ventricular myocardium. The present approach is thus crucial for improved understanding and performance in cardiac modeling in healthy, diseased, and treatment scenarios.

Original languageEnglish (US)
Article number103508
JournalJournal of the Mechanical Behavior of Biomedical Materials
StatePublished - Mar 2020


  • Constitutive modeling
  • Inverse modeling
  • Optimal experimental design

ASJC Scopus subject areas

  • Biomaterials
  • Biomedical Engineering
  • Mechanics of Materials


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