Mechanical energy (ENG) required by a time-varying elastance model of the ventricle was compared with oxygen consumption per beat (VO2) of the canine left ventricle contracting under a variety of loading conditions. ENG needed for this model to increase its elastance during systole is shown to be equal to the sum of the potential energy built in the elastance during systole plus the external mechanical stroke work. This ENG is equivalent to the area (PVA) bounded by the end-systolic and end-diastolic P-V curves and the systolic limb of the P-V loop trajectory in the P-V plane. There was a high correlation (r = 0.89) between VO2s documented in the literature and PVAs assessed by the author from the accompanying P-V data from both isovolumic and ejecting contractions in 11 hearts. A linear regression analysis yielded an empirical equation: VO2 (ml O2/beat) = a . PVA (mmHg . ml/beat) + b, where a = 1.37 X 10(-5) and b = 0.027, which can be used to predict VO2 from PVA. A preliminary experimental study in my laboratory confirmed the validity of this empirical equation.
Multi-robot energy-aware coverage control in the presence of time-varying importance regions
