Numerical models, able to simulate the response of the human cardiovascular system (CVS) in the presence of an implantable rotary blood pump (IRBP), have been widely used as a predictive tool to investigate the interaction between the CVS and the IRBP under various operating conditions. The present study investigates the effect of alterations in the model parameter values, that is, cardiac contractility, systemic vascular resistance, and total blood volume on the efficiency of rotary pump assistance, using an optimized dynamic heart-pump interaction model previously developed in our laboratory based on animal experimental measurements obtained from five canines. The effect of mean pump speed and the circulatory perturbations on left and right ventricular pressure volume loops, mean aortic pressure, mean cardiac output, pump assistance ratio, and pump flow pulsatility from both the greyhound experiments and model simulations are demonstrated. Furthermore, the applicability of some of the previously proposed control parameters, that is, pulsatility index (PI), gradient of PI with respect to pump speed, pump differential pressure, and aortic pressure are discussed based on our observations from experimental and simulation results. It was found that previously proposed control strategies were not able to perform well under highly varying circulatory conditions. Among these, control algorithms which rely on the left ventricular filling pressure appear to be the most robust as they emulate the Frank-Starling mechanism of the heart.