Transmural Myocardial Deformation in the Canine Left Ventricle: Normal in Vivo Three-Dimensional Finite Strains

To examine transmural finite deformation in the wall of the canine left ventricle, closely spaced columns of lead beads were implanted at a single site on the left ventricular free wall. The three-dimensional coordinates of these myocardial markers were obtained with highspeed biplane cineradiography. Any four noncoplanar markers forming small tetrahedral volumes (±0.1 cc) were used to calculate finite normal and shear strains with respect to a cardiac coordinate system at end diastole. Due to the symmetry of the finite strain tensor, the algebraic eigenvalue problem could be solved to compute principal strains and the directions of the principal axes of deformation with respect to the reference coordinates. An examination of the principal strains in a number of tetrahedra in five animals indicates that deformation increases with depth beneath the epicardium. For example, the transmural variation of principal shortening strain averages −0.014 ± 0.009 per 10% increment in thickness from epicardium to endocardium. Furthermore, shortening and thickening strains at midwall and deeper are too large (0.10 to 0.40) to be described accurately by infinitesimal theory. These strains are often accompanied by substantial in-plane and transverse shears which are not predicted by typical membrane or shell theories, indicating that these theories must be applied with caution when computing indices of regional ventricular performance. The directions of the principal axes of shortening vary substantially less than the fiber direction varies across the wall (20-40 compared with 100-140 for fiber direction), supporting the concept that there are substantial interactions between neighboring fibers in the left ventricular wall.