An approach to single-beat estimation of Emax as an inverse problem

The present study has derived a new method for estimating the maximum value (E_max) of the ventricular elastance (E(t)) without direct measurement of the ventricular volume (V(t)) by regarding the estimation process as an inverse problem. The method can estimate E _max in a single beat without any change in preload or afterload by measuring the ventricular pressure (P(t)) and outflow (i(t)) which is much easier to measure than V(t). This method is based on two assumptions that E(t) can be approximated by at+b and that V_ed-V₀=I(t)+P(t)/E(t) holds for any t during the ejection period, where V_ed is the end-diastolic volume, I(t) is the integrated value of i(t) and V₀ is the volume axis intercept of the regression line of the end-systolic pressure-volume relation. In vivo experiments using two adult goats resulted in small mean equation error with respect to V_ed-V₀ less than about 5% of the stroke volume of each heart beat. This implies that the proposed method is practical enough to monitor cardiac function in actual clinical settings