Description of LV pressure-volume relations by time-varying elastance and source resistance

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Abstract
If the left ventricle (LV) behaves as a time-varying elastance [E(t)] that is independent of load, then definition of E(t) during normal ejecting beats should permit accurate prediction of LV pressure (LVP) during a maximally afterloaded (isovolumic) beat. We tested this hypothesis in six dogs preinstrumented to measure LVP and aortic flow (Q) and to determine LV volume (V) from three dimensions. LVP and V were varied by caval occlusions. These data were used to determine E(t) and minimal volume required to generate pressure (Vo) at 10-ms intervals during systole using a simple E(t) model, P(t) = E(t) [V(t)-Vo], where P(t) is LVP at any time after the onset of contraction, and V(t) is the LV volume at t. LVP was measured during isovolumic beats generated by sudden balloon occlusion of the ascending aorta. The simple E(t) model accurately predicted isovolumic LVP during the first 70 ms of systole (r = 0.99) and also the end-systolic LVP but underestimated LVP during midsystole by 48 +/- 5 (SD) mmHg (P less than 0.05). When a pressure-dependent source resistance (K = 0.0015 s/ml) was added to the model to reduce LVP in proportion to Q, such that P(t) = E(t) [V(t)-Vo] X [1 - KQ]), LVP during the isovolumic beat was accurately predicted throughout systole (r = 0.99). However, the time to develop peak isovolumic pressure was 22 +/- 7 ms less than predicted. Similar results were obtained during inotropic stimulation with dobutamine in five animals.