Passive Elasticity of the Human Left Ventricle

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Abstract
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-CAD 1 ), moderate to severe CAD 2 , and mild to moderate CAD 3 . Utilizing precise pressure volume relationships, the natural elastic stiffness (dσ sp. /dε 2 ) for a spherical model and the stiffness constant K 2 were evaluated. In addition, stress-strain relationships for ellipsoid model were utilized for evaluation of the diastolic stiffness and the stiffness constants b 1 and K 3 as obtained for the modified Lagrangian strain (L-L 1 )/L 1 , and the natural strain Loge(L/L o ), respectively. The constants K 2 , b 1 and K 3 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-CAD 1 ); 59.5 ± 9.2, 32.7 ± 3.9 and 33.2 ± 3.9 for six patients with moderate to severe CAD (CAD 2 ) and 35.5 ± 7.3, 24.8 ± 6.3 and 25.4 ± 6.3 for nine patients with mild to moderate CAD (CAD 3 ). The end-diastolic passive elastic stiffness E 2 ed (sphere-natural) and E 3 ed (ellipsoid-natural) were 402 ± 55 g/cm 2 and 526 ± 95 g/cm 2 for the normals, 519 ± 250 and 555 ± 250 g/cm 2 for the IH group, 2420 ± 437 and 3142 ± 680 g/cm 2 for the CHF-CAD, group, 500 ± 166 and 525 ± 140 g/cm 2 for the CAD 2 group, and 352 ± 93 and 506 ± 180 g/cm 2 for the CAD 3 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.