Ejection Fraction (EF) is an important parameter that is used in the diagnosis of heart failure. It provides a measure of the ability of the heart to pump blood into the circulatory system. For patients implanted with a continuous flow left ventricular assist device (LVAD), the standard definition of EF provides a measure of the combined ability of both the heart to pump blood through the aortic valve and the LVAD to pump blood continuously out of the left ventricle both into the circulatory system. In this paper, we introduce a new concept of EF, labeled Aortic Valve Ejection Fraction (or AVEF) which provides an accurate measure of only the ability of the heart to pump blood through the aortic valve while the LVAD is actively running. We investigate the benefits of AVEF and its relation to the LVAD speed using a well-established mathematical model of an LVAD-assisted left ventricle. We compare the sensitivities of the new AVEF index and the standard EF index to changes in heart contractility over a wide range of after loads. Our results show that AVEF is more sensitive to changes in heart contractility than EF. At a typical LVAD speed of 4,000RPM, a 10% improvement in heart contractility over time for a patient with congestive heart failure yields 13.20% increase in AVEF, while the same increase in contractility yields only 7.52% increase in EF. The AVEF index could provide a reliable, non-invasive mechanism for monitoring improvements in heart contractility for patients implanted with LVAD.