Comparison of Directly Measured Left Ventricular Wall Stress and Stress Calculated from Geometric Reference Figures

Abstract

Mean left ventricular wall force was determined with a calibrated transmural auxotonic strain gauge in the left ventricle of six anesthetized, open-chest dogs with intact circulation. The gauge was oriented in the plane of the minor left ventricular equator, midway between the papillary muscles. Left ventricular internal volume was derived from the passive pressure-volume curve of the arrested heart and calculated mean wall stress was derived both from spherical and ellipsoidal reference figures for the left ventricle and compared with measured forces. Control left ventricular end-diastolic pressure averaged 3.0 ± 0.6 mm Hg (SE). At this level of end-diastolic pressure, measured peak wall stress averaged 97.2 ± 14.4 g/cm 2 , whereas calculated peak wall stress averaged 79.3 ± 9.9 and 118.6 ± 12.9 g/cm 2 for the spherical and ellipsoidal models, respectively. Measured end-diastolic wall force values averaged 9.4 ± 4.5 and 29.2 ±8.1 g/cm 2 at an end-diastolic pressure of 3.0 and 12.3 mm Hg, respectively. In all cases, stress values calculated from spherical reference figures for the left ventricle were significantly lower than those measured directly. In four other experiments, using right heart bypass, the ventricular septum was exposed and active wall force was determined at two or more sites on the left ventricular minor equator. Wall stress at these sites differed by an average of 15.3%, indicating that stresses around the minor equator are relatively uniform. These studies lend validity to the application of geometric models in the calculation of mean wall stress and favor the application of an ellipsoid for the geometric reference figure. KEY WORDS auxotonic force gauge average left ventricular wall force Laplace relationship major axis stress ellipsoid of revolution• The recent interest in assessing cardiac performance in terms of muscle function has provided a stimulus for attempting to evaluate stress and strain within the left ventricular wall. Various techniques have been used to

Impaired thickening of nonischemic myocardium during acute regional ischemia in the dog.

“…After total coronary occlusion in the experiments, the extent of ischemia, expressed as the percentage of the left ventricular cross-sectional circumference, was 35.0 + 5.3%. The mean distances from the ischemic border to the centers of the adjacent 1, adjacent 2, and 25.0 ± 2.0% (p < .001). The crosssectional left ventricular shape at end-systole after the onset of regional transmural ischemia became elongated and distorted (figure 2).…”

“…Although regional stress has been measured directly,24 25 Bogen et al31 used the finite element theory to model the human left ventricular cross section damaged by regional transmural infarction. They estimated circumferential myocardial stress to be greater in the adjacent regions than in the remote ones, where it coincided with stress estimates for the noninfarcted heart.…”

Left ventricular adaptation to sustained pressure overload in the conscious dog.

“…The leftward displacement of the end-systolic stress-diameter relationship thus represents an increased inotropic state of a myocardium subjected to a sustained pressure overload. The calculated equatorial wall stress has been shown to correlate well with directly measured wall stress when an ellipsoidal model of left ventricular cavity is used (Burns et al, 1971). This formula does not take into account the septum-free wall diameter which is supposed to be equal to the anteroposterior diameter.…”

The deformational characteristics of the left ventricle in the conscious dog.

“…As first hypothesized by Woods (1892) and recently verified by several investigators (Hefner et al, 1962;Burns et al, 1971;McHale and Greenfield, 1973), the geometry of the ventricular chamber is a major determinant of the force within the ventricular wall. This principle is an embodiment of the Laplace relationship (Laplace, 1839) which predicts that the tensile stress within any shell is a function of the distending pressure, the radii of curvature, and the mural thickness.…”