Complex distributions of residual stress and strain in the mouse left ventricle: experimental and theoretical models

Abstract

Most soft biological tissues, including ventricular myocardium, are not stress free when all external loads are removed. Residual stress has implications for mechanical performance of the heart, and may be an indicator of patterns of regional growth and remodeling. Cross-sectional rings of arrested ventricles opened up when a radial cut was made (initial mean opening angles were 64 +/- 17 degrees), but further circumferential cuts revealed the presence of additional residual stresses in the tissue with further opening of the rings. In normal mouse hearts, the inner half of a short-axis ring opened more than the outer half, and this change was dependent on apex-base location. At the apex the inner section vs. outer section opening angles were 226 +/- 47 degrees vs. 89 +/- 28 degrees, while at the base the same two angles were 160 +/- 30 degrees vs. 123 +/- 35 degrees. A simple theoretical cylindrical shell model with incompressible hyperelastic material properties was used to model the experimental deformations based on the cutting experiments. The model predicts different residual stress fields depending on the nature of the opening after the circumferential cut (which is done after the conventional radial cut). The observed opening angles were consistent with steep stress gradients near the endocardium compared with those predicted if the first cut was assumed to relieve all residual stresses. These results imply a more complex distribution of residual stress and strain in ventricular myocardium than previously thought.

The visceral pericardium: macromolecular structure and contribution to passive mechanical properties of the left ventricle

“…However, the structures of the two layers were similar with more elastin and less collagen found in the endocardial layers (see Figs. 1-3), consistent with the more extensive opening angles found with endocardial sections than with epicardial sections by Omens et al (24), which we confirmed in this study (data not shown). Thus, the endocardial layer of elastin may also contribute to the net residual strain of the myocardium; however, we were not able to confirm this directly due to the inability to dissect this layer free from the wall.…”

“…However, our results clearly demonstrate that the VP has a significant impact on the opening angle and, therefore, must make a major contribution to the residual stress of the LV. The increased opening angles found in epicardial portions of myocardium slices are consistent with the VP being an important factor in the residual stress found in the resting heart (24). This concept is also supported by the report by Omens et al (25), which showed that the opening angle does not change during pressure overload despite significant cardiomyocyte hypertrophy.…”

“…Although the opening angle may not be a complete description of the residual stress, it does reflect the overall level of residual stress in the myocardium (24). The opening angle is a measure of two-dimensional residual strain, which quantifies the circumferential deformation of the LV slice when the residual stress is relieved.…”

Computational Biomechanics of Soft Biological Tissue

“…They argued that myocardial laminae may be the principal residualstress-bearing structures in the LV. A recent experimental and theoretical study by Omens, McCulloch and Criscione (2003), on cross-sectional rings of arrested mouse ventricles showed that further stress is relieved by making a circumferential cut after the radial cut. The cutting experiments were analyzed by a cylindrical shell model with incompressible hyperelastic material properties.…”

Steady diffusion of an ideal fluid through a pre-stressed and reinforced hollow conduit subjected to combined finite deformations

“…Generally, residual strain/stress in anisotropic hyper elastic conduit, such as classical tubes, some specific prosthetic devices and arteries, can be characterized by the opening angle H 0 of the sector-like cross-section. This phenomenon has been known in arterial wall for at least 40 years and residual strain/stress has implication not only for stress gradients such as in classical conduit (elastomeric), but also for growth and remodeling in the living tissue (Huang et al, 1998;Omens et al, 2003). In addition to their ability to homogenize the stress field in the arterial wall, residual strains make arteries more compliant and thereby improve their performance as elastic reservoirs and ensure more effective local control of the arterial lumen by smooth muscle cells.…”