Subepicardial fiber strain and stress as related to left ventricular pressure and volume

In a mathematical model of the mechanics of the left ventricle (LV) by Arts et al. (1), assuming uniformity of fiber stress (sigma f) and fiber strain (delta epsilon f) in the wall during the ejection phase, fiber stress and fiber strain were related to LV cavity pressure (Plv), LV cavity volume (Vlv) and wall volume (Vw) by the following pair of equations: sigma f = Plv (1 + 3 Vlv/Vw) and delta epsilon f = 1/3 delta ln (1 + 3 Vlv/Vw). The ratio of Vlv to Vw appeared to be the most important geometric parameter, whereas the actual LV shape was of minor importance. The relationships on fiber strain and stress were evaluated experimentally in six anesthetized open-chest dogs during normal and elevated (volume loading) end-diastolic LV pressure. Subepicardial fiber strain was measured simultaneously in 16 adjacent regions of the LV anterior wall, using optical markers that were attached to the epicardial surface and recorded on video. Changes in Vlv were measured by use of four inductive coils sutured to the LV in a tetrahedric configuration. Vw was measured postmortem. During control as well as hypervolemia the following results were found. At the anterior free wall of the LV, the slope of the estimated linear relationship between measured and calculated fiber strain was 1.017 +/- 0.168 (means +/- SD), which is not significantly different from unity. Calculated fiber stress corresponded qualitatively and quantitatively with experimental results reported on isolated cardiac muscle. Calculated subepicardial contractile work per unit of tissue volume was not significantly different from global pump work as normalized to Vw. These findings support the assumption of homogeneity of muscle fiber strain and stress in the left ventricular wall during the ejection phase. Furthermore, average values of fiber stress and strain can be estimated on the basis of measured left ventricular pressure and volume.