Passive Elasticity of the Human Left Ventricle
The "Parallel Elastic Element"
Pressure-volume (PV) and stress-strain relationships (σ-ε) were utilized for evaluation of stiffness changes in the human left ventricle. A total of 45 patients were studied with data available from routine cardiac catheterization. They were divided into eight groups from which five were chosen for statistical comparison. These were the groups of normal, idiopathic hypertrophy without obstruction (IH), congestive heart failure in severe coronary artery disease (CHF-CAD1), moderate to severe CAD2, and mild to moderate CAD3. Utilizing precise pressure volume relationships, the natural elastic stiffness (dσsp./dε2) for a spherical model and the stiffness constant K2 were evaluated. In addition, stress-strain relationships for ellipsoid model were utilized for evaluation of the diastolic stiffness and the stiffness constants b1 and K3 as obtained for the modified Lagrangian strain (L-L1)/L1, and the natural strain Loge(L/Lo), respectively. The constants K2, b1 and K3 were 20.3 ± 1.5, 15.0 ± 2.4 and 15.8 ± 2.3 for eight normal patients; 34.5 ± 7.9, 18.3 ± 3.4 and 19.0 ± 3.5 for seven patients with idiopathic hypertrophy; 101.2 ± 24.2, 61.0 ± 13.0 and 62.3 ± 13.0 for six patients with severe CAD and CHF (CHF-CAD1); 59.5 ± 9.2, 32.7 ± 3.9 and 33.2 ± 3.9 for six patients with moderate to severe CAD (CAD2) and 35.5 ± 7.3, 24.8 ± 6.3 and 25.4 ± 6.3 for nine patients with mild to moderate CAD (CAD3). The end-diastolic passive elastic stiffness E2 ed (sphere-natural) and E3 ed (ellipsoid-natural) were 402 ± 55 g/cm2 and 526 ± 95 g/cm2 for the normals, 519 ± 250 and 555 ± 250 g/cm2 for the IH group, 2420 ± 437 and 3142 ± 680 g/cm2 for the CHF-CAD, group, 500 ± 166 and 525 ± 140 g/cm2 for the CAD2 group, and 352 ± 93 and 506 ± 180 g/cm2 for the CAD3 group. The results indicate that: 1) all stiffness constants correlated with each other very well and all are sensitive to the magnitude of the damage to the individual myocardium caused by a given disease state; 2) the ellipsoid-natural strain equation as developed in this study, which is more appropriate for biological materials, has the advantage of being the simplest of all other equations; 3) stiffness constants depend upon the quality of a given thick wall and not upon the thickness per se; 4) end-diastolic elastic stiffness may remain normal due to opposing effects of compliance, dilatation and hypertrophy; 5) the exponential part of the diastolic stress-strain curve describes only a partial mechanism by which resting force of the intact heart is explained.
- Intact human heart
- Pressure volume relationships
- Coronary artery disease
- Wall stress
- Received January 29, 1974.
- Accepted May 15, 1974.
- © 1974 American Heart Association, Inc.