Comparison of Calculations of Left Ventricular Wall Stress in Man from Thin-Walled and Thick-Walled Ellipsoidal Models

Hood, William P.; Thomson, Walter J.; Rackley, Charles E.; Rolett, Ellis L.

doi:10.1161/01.res.24.4.575

Cited by 75 publications

(30 citation statements)

References 18 publications

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“…His results indicate that for typical ventricular geometry, these effects are negligible except near the apex of the ventricle. Hood et al (16) have compared Sandier and Dodge's results with average stresses obtained from Wong and Rautaharju and confirm the overestimation of average stress (approximately 10%) by the Sandier and Dodge formula.…”

Section: Falsetti Mates Grant Greene Bunnellmentioning

confidence: 73%

Left Ventricular Wall Stress Calculated from One-Plane Cineangiography

Falsetti

Mates

Grant

et al. 1970

Circulation Research

195

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Left ventricular dimensions from routine clinical one-plane cineangiograms were combined with left ventricular pressure measurements to permit calculation of left ventricular wall stresses. The 25 patients included 12 with normal left ventricular dynamics, 6 with volume overload, 3 with outflow obstruction, and 4 with cardiomyopathy. Average stresses calculated on the basis of an ellipsoid model agreed with average values obtained from the exact solution of a thick-walled elastic ellipsoidal shell. Peak values were 150 to 625 g/cm 2 in the circular direction and 75 to 365 g/cm 2 in the longitudinal direction. A fiber-corrected stress was defined which represents a force per muscle fiber. The variation in fiber-corrected stress during the cardiac cycle may be considerably different from the variation in simple stress.The force-velocity characteristics of circular fibers for the 25 patients are presented. The data on peak wall stress overlap in the four groups of patients. Peak velocity of circumferential fiber shortening varied from 0.44 to 0.63 lengths/sec in patients with myocardial weakness and varied from 0.74 to 2.56 lengths/sec in the other patients. Contractile element velocity was determined during ventricular ejection when the rate of force change equaled zero. Contractile element velocity of shortening was 0.22 to 0.32 lengths/sec in the cardiomyopathy group and 0.50 to 1.32 lengths/sec in the other patients. ADDITIONAL KEY WORDScontractile element velocity of shortening left ventricular wall thickness cardiac muscle mechanics B The force developed by a contracting muscle is a function of the velocity of contraction. The force-velocity relation was first determined for skeletal muscle (1, 2) and more recently has also been determined in isolated cardiac muscle (3-5). The mechanical behavior of the intact heart is a complicated function of its geometry as well as of the contractile behavior of individual muscle fibers. The performance of the heart may be determined by cineangiography

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Section: Falsetti Mates Grant Greene Bunnellmentioning

confidence: 73%

Left Ventricular Wall Stress Calculated from One-Plane Cineangiography

Falsetti

Mates

Grant

et al. 1970

Circulation Research

195

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“…Despite wide variations in techniques and assumptions, it is interesting that very little quantitative difference appears to exist between myocardial wall stresses calculated from either thick-walled or thin-walled ellipsoidal reference figures (7,10,11,30,32). The results of the present study reinforce these conclusions and, in addition, have shown that there are relatively minor differences between directly measured myocardial wall stresses and wall stress calculated assuming relatively simple geometric reference figures, a sphere or ellipsoid, and thin-wall theory for the basis of the calculation.…”

Section: Discussionmentioning

confidence: 99%

“…More recently, such analyses have been extended to include consideration of fiber angle distribution within the left ventricular wall (8,9). There are indications that some reference figures may be more appropriate than others (3,(10)(11)(12). However, all of this evidence is indirect and does not involve direct measurement of force.…”

mentioning

confidence: 99%

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

Burns

Covell

Myers

et al. 1971

Circulation Research

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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

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“…8), that it is tempting to interpret it in terms of physiologic functioning of myocardial muscle. The way to do so would be through the construction of a detailed ventricular model, based on actin-myosin filament interaction (36,42,49,56,78), and ventricular geometry (17,30,41,46,54,65,66,79,81), as well as anatomy (4,81,90,92,104), and electrophysiology (10). However, such studies seldom attempt to quantitatively predict ventricular performance in terms of compressed data models as the present three-compartment model.…”

Section: Co T a + Ementioning

confidence: 99%