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

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.