The use of a rotary Left Ventricular Assist Device (LVAD) as a bridge-to-recovery treatment is gaining considerable attention in the LVAD research community. Using a mathematical model of the cardiovascular-LVAD system, this paper intends to define the critical control parameters in terms of power and rotational speed of the LVAD to ensure normal dynamics of the aortic valve for different levels of patient's activity and severity of heart failure. The effects of permanent closure of the aortic valve on the hemodynamics of the patient and the pump flow characteristics, if the critical control values are exceeded, are also examined. Additionally, LVAD power and speed control parameters that yield a given percentage of the cardiac cycle during which the aortic valve remains open are examined indicating that the severity of the heart failure is a very important factor in deciding the appropriateness of the LVAD as a bridge-to recovery treatment.