Muscle stiffness determined from canine left ventricular pressure-volume curves.

Abstract

We measured pressure-volume curves in nine excised dog ventricles and stress-strain curves in two to five muscle specimens from each ventricle to verify a derived formula that relates muscle stiffness to the ventricular pressure-volume curve. The assumptions underlying this formula are: (1) the ventricle is a uniform spherical shell, (2) all muscle fibers carry average stress and deform as if they were at the midwall, (3) static equilibrium exists, (4) internal pressure induces the only load, and (5) the muscles exhibit an exponential stress-strain curve given by the equation a( i) = a(e B * ' -1), where a = stress, e = strain, and a and /S* are constants. There was no significant difference between the stiffness constant, /8*, inferred from the left ventricular pressure-volume curves (14 ± 4.3 [SD]) and that measured directly from the muscle stress-strain curves (16 ± 2.8).• Growing interest in describing the left ventricle's diastolic pressure-volume relationship has led many investigators to propose stiffness indexes. To date, however, the relationship between these indexes of the ventricular pressure-volume curve and the stiffness of the muscle itself remains cloudy. For example, there is not yet agreement on the question of whether changes in the diastolic pressure-volume curve that accompany disease arise from changes in the elasticity of the muscle itself (1-4), geometric effects associated with hypertrophy or dilation (5, 6), or other mechanisms (7). These controversies arise because of a lack of an experimentally validated and logically derived equation describing the ventricular pressurevolume relationship in terms of the muscle's nonlinear elasticity. We have derived such an equation and verified that the stiffness parameter computed from the pressure-volume curve is the same as that exhibited by muscle strips from the same heart. This pressure-volume equation follows from five assumptions about the left ventricle. (1) It behaves as a uniform-thickness spherical shell which does not contract. (2) All of the muscle fibers carry the average stress and deform as if they were at the midwall.

Losartan-Dependent Regression of Myocardial Fibrosis Is Associated With Reduction of Left Ventricular Chamber Stiffness in Hypertensive Patients

“…LV stiffness is governed by a complex interplay of myocardial stiffness (largely related to the tissue collagen content), 23 ventricular geometry (hypertrophy 24 and distension 25 ), and myocardial relaxation. 26 Our findings that K LV in hypertensive patients is related to CVF but not to the degree of LV hypertrophy and relaxation abnormalities and that LV volumes were not increased in these patients (data not shown) strongly suggest that myocardial fibrosis is the main determinant of LV stiffness in essential hypertension.…”

Hydroxyproline and passive stiffness of pressure-induced hypertrophied kitten myocardium.

“…However, we found that with high sensitivity tracings, measurements of muscle length at the point where resting stress first rises above zero are reproducible, i.e., ±8%. Furthermore, Glantz and Kernoff (11) have shown that d is relatively insensitive to small changes in initial muscle length.…”

“…We assessed passive stiffness from the stress-strain relationship calculating the elastic constants a and ,8 as described by Glantz and Kernoff (11). Because the stress-strain relationship of cardiac muscle is monoexponential over the physiologic range of stress (11,12), the elastic constants can be derived from: a = a (e#' -1) where a = force/instantaneous cross sectional area and e (Lagrangian strain) = 1 -10/10, 1 being unstressed muscle length. We also calculated the tangent modulus or elastic stiffness (da/ de) from do/de = ,a + #a (11).…”

“…Because the stress-strain relationship of cardiac muscle is monoexponential over the physiologic range of stress (11,12), the elastic constants can be derived from: a = a (e#' -1) where a = force/instantaneous cross sectional area and e (Lagrangian strain) = 1 -10/10, 1 being unstressed muscle length. We also calculated the tangent modulus or elastic stiffness (da/ de) from do/de = ,a + #a (11). Since the stress-strain relationship is exponential, elastic stiffness is linearly related to stress.…”

Ventricular pressure-volume curve indices with end-diastolic pressure.

“…Glantz and Kernoff 17 showed such computations were possible given enough data, but even their theory failed when confronted with the limited amount of information possible in a clinical setting. …”