Pressure-volume (PV) and stress-strain relationships (a-e) 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,), moderate to severe CAD2, and mild to moderate CAD3.Utilizing precise pressure volume relationships, the natural elastic stiffness (da80./dE2) 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 bi and K3 as obtained for the modified Lagrangian strain (L-L,)/L, and the natural strain Loge(L/Lo), respectively. The constants K2, b, 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); Several methods have been employed for analysis of left ventricular diastolic con;pliance or elasticity. Some of them related simple pressure difference to volume difference AP/zV or z1V/AP.4 5 It was soon 609
et al.4 and Hamrell et al.5 that passive elastic stiffness constants are elevated in hypertrophy due to pressure overload. The conclusions drawn from the studies of Grimm et al. 6 and Spann et al.7 must be considered with caution since they employed inappropriate definitions for strain in their analyses. This writer has reanalyzed the raw data of Spann et al. and finds that their results are in agreement with the other investigators.4 5 However, an analysis of data obtained from the animal studies of Taylor and his associates8' 9 indicates that stiffness constants may remain normal in hypertrophy due to volume overload. 2. Present studies by this author and Dr. R. F. Janz based on large deformation theory reveal that (1) stiffness-stress relations are curvilinear over the entire range of diastole and are only approximately linear over the latter portion of diastole. Thus one should not define c in the relation E = ka + c to be the stiffness at zero stress.(2) Qualitative results are similar to those obtained from a linear elastic theory such as that presented by the authors.(3) Passive elastic behavior of cardiac muscle conceptually may be represented by two nonlinear elastic springs in parallel, one being more compliant than the other for lengths near zero stress and less compliant than the other for lengths near the optimal length. 3. K is sensitive to volume elasticity VdP/dV and the volume/mass ratio and not the thickness per se. 4. The use of a modified Lagrangian strain is not always satisfactory since ventricles do not operate over common stress levels in many cases. No such problem is encountered if the natural strain definition is employed. This definition also has the advantage in that zero stress dimensions are not required in the computations based on linear elastic theory. 5. If the constant a is normalized to left ventricular mass, it would correlate better with the K constants. 6. In the computation of elastic stiffness, average strain or midwall strain should be associated with average stress. If this principle is followed, the authors will find that their K3 values would be in closer agreement with the K2 valujes. Thus the analysis presented by the authors should be modified in the following manner: (1) define natural strain to be (3 = loge (R/R0) where R,R0 are the instantaneous and zero stress midwall radii or semi-minor axes, i.e., dE3 = dR/R, and R = L + h/2 (h = wall thickness).(2) Plot the midwall stress a (based on a sphere or ellipsoid) as a function of the instantaneous midwall radius R and, employing a nonlinear regression analysis, express a as an exponential or polynomial function of R.(3) Define elastic stiffness as E = da/dE3 = R dr/dR which may then be plotted against the stress rand a relation on E = kr + c obtained by a linear regression analysis.Finally, it is recommended that P-V relations be obtained with the aid of high fidelity pressure transducers and that the simple P-V relation employed by this writer not be used.
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