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

Abstract

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.

A comparison of two quasi‐static computational models for assessment of intra‐myocardial injection as a therapeutic strategy for heart failure

“…As the incompressible constraint cannot be enforced by Abaqus in an explicit solution scheme, 29 the myocardium was modeled using the so-called slightly compressible approach, which has recently been shown to be more accurate to represent the myocardium. 35 The run time of each simulation was approximately 8 hours on a CentOS cluster with three nodes, each consisting of a Xeon E5-2650 processor.…”

“…Mass scaling was used to provide feasible computation times, and the kinetic energy of the system was monitored to ensure that the response was quasistatic (ie, kinetic energy was less than 5% of the internal energy). As the incompressible constraint cannot be enforced by Abaqus in an explicit solution scheme, the myocardium was modeled using the so‐called slightly compressible approach, which has recently been shown to be more accurate to represent the myocardium . The run time of each simulation was approximately 8 hours on a CentOS cluster with three nodes, each consisting of a Xeon E5‐2650 processor.…”

Novel hyperelastic models for large volumetric deformations

“…Graphene aerogels can also be 3D printed [64] allowing for the creation of highly elastic, deformable, and complex lattices structures. Formulation 3 can also be used to simulate non-monotonic volumetric stiffening of compressible biological materials, such as arteries [65], and the myocardium [66]. Formulation 3 can also be extended to account for plastic buckling in the plateau region (as observed for polypropylene foams [67], metallic foams [68], and trabecular bone [69,70].…”

An orthotropic electro-viscoelastic model for the heart with stress-assisted diffusion

“…Moreover, full incompressibility of the tissue will be enforced in the present framework, and this has some advantages associated with the mathematical and numerical structure of the system. Although biological tissues possess a complex porous structure, compression features are still being systematically investigated ex-vivo, and a more comprehensive answer on the subject is still needed [51].…”