Engineering Mechanics for Successive States in Canine Left Ventricular Myocardium

Abstract

The relations between end-diastolic (D) and end-systolic (S) cavitary volumes (V c), wall volumes (V w), and cavitary dimensions have been studied in the canine and human left ventricle. However, the models selected for left ventricular myocardium do not represent the real heart adequately for a fiber-by-flber analysis of fiber orientation and sarcomere length during successive states of the ejection cycle. In this study, the endocardial and epicardial surfaces were postulated to be a nested set of truncated ellipsoidal shells of revolution where wall volumes were preserved from D to S. Shell dimensions on the semiminor and semimajor axes, R and Z, respectively, were related to V c and V w by two representations: confocal and nonconfocal. If the focal length C = (Z 2-R 2)t and C is the same for each shell, then the shells are confocal, otherwise they are nonconfocal. From measured V c , V w , and epicardial Z in D, shell dimensions were calculated for states D and S, using both confocal and nonconfocal representations , and compared with the measured dimensions, When no empirical corrections were made, the calculated endocardial R in S underestimated the measured R in S by 12%; moreover, the calculated epicardial R in S overestimated the measured R in S by 4%. Endocardial and epicardial C measured 3.73 ± 0.33 (SE) cm and 3.79 ± 0.34 cm, respectively, in D and 3.77-0.11 cm and 3.71 ±0.10 cm, respectively, in S. KEY WORDS cavitary volumes wall volumes confocal ellipses papillary muscle volumes ellipsoid of revolution grid dimensions left ventricular wall thickness eccentricity of ellipse focal length of ellipse • The shape of the left ventricular myocardium can be likened to that of an eggshell with its top cut off: the aortic and mitral valve openings represent the rim (the base) and the wall is thickest at the greatest circumference (the equator) and thinnest at the bottom (the apex) (Fig. 1). The left ventricular wall is the site at which local fiber orientation, sarcomere length, and fiber stress should be measured; a mathematical description is needed. Eighty years ago, the left ventricular wall was viewed as a curved membrane with two principal radii of curvature and a finite thickness (1). There were no systematic intramural data and fiber stresses were thought to be uniformly distributed across the thickness of the wall. Since that time, great strides have been made in mapping the interior of this structure at both the gross (2-6) and the ultrastructural level (7-10). Yet the simple membrane concept still prevails (11), although some investigators depict the left ventricle as a sphere (12) or as a full ellipsoid (13-15) with uniform wall thickness. A sophisticated representation, devised by Dieudonne (16), assumes that the endo-cardial and epicardial surfaces are confocal ellip-soids of revolution, thus realistically accounting for the longitudinal variation in wall thickness. Because of the lagging development of realistic models, clinical techniques for measuring the wall do not adequately describe the m...

Conformal piezoelectric energy harvesting and storage from motions of the heart, lung, and diaphragm

“…3G). This behavior, for 0°and 45°, is expected because the myocardial tissue of the heart is anisotropic and contracts in a generally circumferential direction (26) with cardiac fibers aligned in a continuous manner from +60°on the endocardium to −60°on the epicardium (27); 90°is clearly out of this range. Theoretically, as shown in Eq.…”

Heart wall myofibers are arranged in minimal surfaces to optimize organ function

“…With the expressions for h ¼ ðx; y; z; θÞ provided in [2][3][4] and with the expression for the normal vector N provided in [5], one can verify that traceðdNÞ¼h∂N∕∂u; ∂h∕∂uiþh∂N∕∂v; ∂h∕∂viþh∂N∕∂w; ∂h∕ ∂wi¼0; ∀fx; y; z; θg, which completes the proof.…”

Embryonic expression of tenascin‐X suggests a role in limb, muscle, and heart development

“…TN-X is expressed in the myocardium during a time that the ventricular wall is undergoing dramatic changes in wall thickness and loading. In the adult ventricle, there is a continuous change in fiber orientation from epicardium to endocardium, and the resulting arrangement of fibers in concentric shells may be important for normal ventricular function (Streeter and Hanna, 1973). It is not known how this pattern of fiber arrangement is established during development, but it is likely that cardiac muscle is patterned by its connective tissue (Noden, 1991).…”