Deformation of the diastolic left ventricle—II. Nonlinear geometric effects

Janz, R. F.; Kubert, Bruce R.; Moriarty, T. Fintan; Grimm, Arthur F.

doi:10.1016/0021-9290(74)90085-2

Cited by 47 publications

(26 citation statements)

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“…1) where the undeformed length of the papillary muscle is set at 80% of the length at maximum developed tension. For physiological pressures the papillary muscle is essentially incompressible; consequently the volume of the papillary muscle remains constant dur- (Janz and Grimm, 1973 ing its deformation. For uniaxial papillary muscle tests, if A is the stretch along the axis of the specimen and L is the stretch transverse to this axis, then the incompressibility condition can be written:…”

Section: Discussionmentioning

confidence: 99%

“…The stress-stretch data for relaxed rat papillary muscle in uniaxial tension tests (Grimm et al, 1970), shown in Figure 1 is taken from Janz and Grimm (1973, Fig. 1) where the undeformed length of the papillary muscle is set at 80% of the length at maximum developed tension.…”

Section: Discussionmentioning

confidence: 99%

“…The stress (true stress, Cauchy stress), S, of Figure 1 was determined from Janz and Grimm (1973, Fig. 1) with the developed tension set equal to 2.5 g at the optimum length (stretched length of papillary muscle at which developed tension is maximum); and A = 1.0 mm 2 (Grimm et al, 1970).…”

Section: Discussionmentioning

confidence: 99%

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The law of Laplace. Its limitations as a relation for diastolic pressure, volume, or wall stress of the left ventricle.

Moriarty¹

1980

Circulation Research

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SUMMARY I made a detailed comparative examination of five mathematical models of left ventricular (LV) mechanics: the Laplace model, Lame model, Valanis-Landel model, Rivlin-Saunders model, and a nonhomogeneous version of the Valanis-Landel model. All five models are used to predict LV pressurevolume (P-V) and pressure-wall stress (P-S) behavior using the same geometric and stress-strain data (rat data is used as an example). These predictions are presented in graphical form for comparison with each other and observed LV P-V behavior. The first model, based on the Law of Laplace, uses the thin wall approximation in three distinct ways, and this approximation is not consistent with LV mechanics. The small deformation and linear stress-strain assumptions of the Lame model also are inconsistent with LV mechanics. Two more homogeneous models (Valanis-Landel and Rivlin-Saunders) avoid the errors of the first two. The discrepancy in the predictions of these two models demonstrates that uniaxial stress-strain data of papillary muscle are insufficient to characterize the multiaxial stressstrain behavior of myocardial tissue. Finally, a nonhomogeneous version of the Valanis-Landel model which explores the variation of myocardial stress-strain behavior needed to achieve constant wall stress is presented. Circ Res 46: 321-331, 1980 AN ACCURATE determination of the interrelationship of pressure, volume, and wall stress of the left ventricle (LV) is an important prerequisite for a fundamental understanding of cardiac mechanics. This interrelationship is a mathematical model which is used to predict wall stress from observed pressure and geometry (Ford, 1976;Rackley, 1976;Mirsky, 1974;Spotnitz and Sonnenblick, 1973;Streeter and Hanna, 1973a, Gould et al., 1972;Falsetti, et al., 1970Falsetti, et al., ,1971 Burns et al., 1971) and stressstrain relations for myocardial tissue from either LV pressure-volume behavior (Glantz, 1976;Rackley, 1976;Fester and Samet, 1974;Mirsky and Parmley, 1973;Lafferty et al., 1972;Diamond et al., 1971), or stress-strain relations of papillary muscle. It also is used to assess myocardial contractility (Falsetti et al., 1971;Hugenholtz et al., 1970) and predict LV volume from pressure (Burns et al., 1971) or vice versa (Sonnenblick and Strobeck, 1977). A mathematical model of LV mechanics is essential for the unified understanding of LV morphology in abnormal and diseased states. It may be based on the Law of Laplace (Woods, 1892), the work of Lame (1866), or the work of others, but whatever the source of the mathematical model, it is important that the assumptions on which it is based are satisfied for the range of deformation and stress-strain behavior exhibited by the LV; otherFrom the Engineering Science and Mechanics Department, University of Tennessee, Knoxville, Tennessee.This investigation was supported in part by U.S. Public Health Service Research Grant HL-14651 from the National Heart, Lung, and Blood Institute.Address for reprints: Thomas F. Moriarty, 317 Perkins Hall-UT, Knoxville, ...

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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The law of Laplace. Its limitations as a relation for diastolic pressure, volume, or wall stress of the left ventricle.

Moriarty¹

1980

Circulation Research

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“…I). 25 - 28> 29 -34~37 Both Equation 2 and more sophisticated models, which include realistic geometry 38 and the effects of large deformations, 39 predict this behavior; it results mostly from the nonlinear relationship between chamber volume and wall deformation. In short, even though the pressure-volume curve looks exponential over short segments, the logic that the muscle's exponential stress-strain relationship requires the heart's pressure-volume relationship to be exponential is incorrect.…”

Section: Basic Mechanicsmentioning

confidence: 99%

Factors which affect the diastolic pressure-volume curve.

Glantz¹,

Parmley²

1978

Circulation Research

357

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“…Even though transversely isotropic or even fully isotropic materials have been proposed for modelling the constitutive behavior of the myocardium [109,128], it is by now well-accepted that orthotropic material models need to be incorporated in more realistic mechanical models of cardiac tissue. For the examples shown in Sect.…”

Section: Passive Hyperelastic Materials Models For Cardiac Tissuementioning

confidence: 99%