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• The study of strips of cardiac muscle has provided much valuable information regarding those factors which determine the force generated during contraction. Interrelationships between force, velocity of shortening, di&stolic stretch, duration of systole, and contractility have been delineated. "5 These findings are not, however, directly and siiiaply applicable to the physiology of the intact heart because the force generated by the myocardium and the corresponding pressure are by no means synonymous. In order to relate the physiology of muscle strips to that of the intact ventricle, the quantitative relation between force in the wall of the ventricle and pressure in the cavity must be known.The importance of such considerations in cardiac physiology has long been recognized. Burton, 10 and Linzbaeh. 11 More recently, Levine and Wagman have discussed the possible influence of the size and shape of the heart on myocardial oxygen consumption, emphasizing the important distinction between the pressure developed by the ventricle and the tension exerted by the fibers. Supported by American Heart Association grant. Work was done during Dr. Hefner's tenure as an Established Investigator of the American Heart Association and Dr. Sheffield's tenure of a TJ. S. Public Health Service Research Fellowship (HF-9775).Received for publication March 30, 1962. lows: Gravitational effects are ignored since they are unimportant in this situation. Consider a static left ventricle of any shape and size containing blood under a given pressure, as in figure 1. Now visualize an imaginary plane through this ventricle as shown in the figure. This imaginary plane divides the ventricle into two parts and passes through a rim of myocardium and a cross-sectional area of the cavity. From elementary hydrostatics it is known that the pressure of the blood in the cavity creates a force in a direction perpendicular to the imaginary plane exactly equal to the product of the pressure (which is force per unit area) times that cross-sectional area of the cavity included in the imaginary plane. The shape of this cross-sectional area of the cavity in our imaginary plane is immaterial, and the size and shape of the rest of the ventricle are also completely without effect on this relation. Since we began by postulating a static ventricle, Newton's laws of motion require that the force mentioned above tending to separate the two parts of the ventricle on each side of the plane be exactly balanced by an equal and opposite force. This equal and opposite force must exist in the rim of myocardium included in the imaginary plane, shown by the stippled area in figure 1. Note that this force exists in the rim of myocardium determined by the imaginary plane, its direction is perpendicular to the plane, and its magnitude is determined only by the pressure and cross-sectional area of the cavity and is independent of the thickness of the wall, the shape or cross-sectional area of the rim, the size or shape of the remainder of the ventricle, the distribution of f...

The frequency equation for longitudinal waves in a viscoelastic tube of infinite length filled with a viscous fluid is solved for the complex wavenumber, k(=k1+ik2). Thus for two modes, Young's mode and Lamb's mode, an explicit expression for k is obtained which yields the phase velocity c(=ω/k1, ω=radial frequency) and the damping constant k2. The formulas for k, c, and k2 are valid for wall thicknesses up to the size of the inner radius of the tube. The approximation as compared with results obtained numerically with an IBM 7040 digital computer from the original frequency equation involves an error which in almost all cases is considerably less than 1.5%. For Lamb's mode, as it was found earlier for the torsional mode, an increase of the fluid viscosity increases the damping at the higher frequencies but decreases the damping at the lower frequencies. The theoretical results are compared with those of experiments in which the longitudinal waves are generated in the fluid and the fluid in its turn moves the wall. The experimental curves thus obtained show the pattern of Young waves, and the agreement with the Young curves obtained from the formulas mentioned above is satisfactory. For torsional waves, formulas for k, c, and k2 analogous to these for longitudinal waves are given.

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