Evaluation of several geometric models for estimation of left ventricular circumferential wall stress

McHale, Philip A.; Greenfield, Joseph C.

doi:10.1016/0002-9149(73)90309-3

Cited by 8 publications

(13 citation statements)

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“…The results of the present study depend integrally upon the validity of the ellipsoidal shell theory used to derive the threedimensional stresses and deformations. This theory has been tested experimentally, and the latitudinal stress calculated from transmural pressure and ventricular dimensions correlated well with the directly measured latitudinal stress (McHale and Greenfield, 1973). In addition, the end-diastolic latitudinal stress calculated previously with this model in the conscious dog (Rankin et al, 1977) was similar to that directly measured by Bums et al (1971).…”

Section: Figure 7 the Relation Between The R/h Ratio And Intracavitarsupporting

confidence: 79%

“…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.…”

mentioning

confidence: 81%

“…This equation has been validated previously in our laboratory (McHale and Greenfield, 1973). The mean tensile stress in the major axis circumference (longitudinal stress) was computed using the equation:…”

Section: Methodsmentioning

confidence: 99%

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

Olsen

Rankin

Arentzen

et al. 1981

Circulation Research

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SUMMARYWe studied left ventricular minor and major axis diameters and equatorial wall thickness in eleven conscious dogs with chronically implanted pulse-transit ultrasonic dimension transducers. Left ventricular tranemural pressure was measured with micromanometers. Left ventricular volume was varied by inflation of implanted vena caval or aortic occluders. The geometry of the left ventricle was represented as a three-dimensional ellipsoidal shell. Left ventricular eccentricity was found to be a linear function of ventricular volume during both diastole and ejection. However, the relationship was not the same for diastole and ejection, and during diastole the left ventricle was more spherical at large volumes and more elliptical at small volumes than during ejection. The rearrangements in geometry observed during isovolumic contraction appeared to be transitional stages from the diastolic to the ejection-phase relationship. Thus, during isovolumic contraction, the left ventricle became more elliptical at large volumes and more spherical at small volumes. These relationships were not altered significantly by increased afterload or inotropic interventions. We also observed that the diastolic deformation of the ventricular chamber occurred in a set and predictable manner that seemed to be determined by the three-dimensional mechanical properties of the myocardium. The geometric interrelationships of the ventricular wall determined the relationship between diastolic transmural pressure and mural stress. These findings probably reflect basic structural characteristics of the myocardium and provide a convenient method for quantitatively representing the dynamic geometry of the left ventricle. Circ Res 49: 843-855, 1981

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Section: Figure 7 the Relation Between The R/h Ratio And Intracavitarsupporting

confidence: 79%

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confidence: 81%

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

Olsen

Rankin

Arentzen

et al. 1981

Circulation Research

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“…The standard relations of linear elasticity are used to derive the stress-strain relations in the myocardium [5,11]. Although the use of linear elasticity has given contradictory results in the past [12], the mathematical approach used in this study has given consistent results. By assuming that near the equatorial region, the myocardium can be approximated by a two-dimensional model, one can assume that the longitudinal strain ε L ≈ 0, Y L ≈ Y t (Young's modulus of elasticity respectively in the longitudinal and transverse directions), and by assuming that the volume of the myocardium is constant the incompressibility condition implies that the Poisson's ratio ν t ≈ 0.5.…”

Section: Mathematical Calculationmentioning

confidence: 82%

Measurement and calculation of the intramyocardial stress

Mihăilescu¹,

Shoucri²

2005

Modelling in Medicine and Biology VI

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By using a servo-nulling mechanism and coated glass micropipettes (20-24 µm OD), intramyocardial stress (IMS) was measured at the base of the left ventricle in isolated working and nonworking cat hearts, perfused with Krebs-Henseleit buffer. Glass micropipettes were placed at various depths inside the left ventricular wall using a micropipette holder and manipulator. Calculation of the IMS is not a simple problem because of the complex structure of the active fibres in the myocardium. However a mathematical approach has been developed that reduces the complexity of this problem. It consists in using the concept of force per unit volume of the myocardium to model the components of the stress generated by the fibers in three orthogonal directions (assuming symmetrical contraction). Important relations are derived between the stress induced by the LVP and the stress induced by the active fibres in the passive medium of the myocardium. Keywords: measurement with micropipette, intramyocardial stress, active and passive stress in the myocardium, left ventricular elastance, active force per unit volume of the myocardium, stress-strain relation in the myocardium.

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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%