This paper intends to define an optimal range for the pump speed of Rotary Left Ventricular Assist Devices (LVADs) that are used in bridge-to-recovery treatments. If the pump is operating within that optimal range, the aortic valve will be working properly (i.e. opening and closing) in each cardiac cycle. The proper operation of the aortic valve is a very important factor in helping the heart muscle recovers. The optimal range varies depending on the severity of the Heart Failure (HF) and the level of activity of the patient. A comparison is shown between the total flow produced as a result of operating the pump within the optimal range and the physiological demand of the patient. The comparison suggests that for cases of mild to moderate HF the flow produced is close to the physiological demand, but in severe cases the flow is significantly less than what the patient requires. Furthermore, our results suggest that data from the pump flow and the left ventricle volume signals can be used to test whether or not the aortic valve is experiencing permanent closure. Also an investigation of the aortic valve opening duration is presented for two cases: first, for mild HF case with varying Heart Rate (HR) and then for fixed HR and mild to severe HF cases. These Simulation results are obtained using a 6(th) order mathematical model of the cardiovascular-LVAD system.