A lumped parameter model of human cardiovascular-implantable rotary blood pump (iRBP) interaction has been developed based on experimental data recorded in two healthy pigs with the iRBP in situ. The model includes descriptions of the left and right heart, direct ventricular interaction through the septum and pericardium, the systemic and pulmonary circulations, as well as the iRBP. A subset of parameters was optimized in a least squares sense to faithfully reproduce the experimental measurements (pressures, flows and pump variables). Our fitted model compares favorably with our experimental measurements at a range of pump operating points. Furthermore, we have also suggested the importance of various model features, such as the curvilinearity of the end systolic pressure-volume relationship, the Starling resistance, the suction resistance, the effect of respiration, as well as the influence of the pump inflow and outflow cannulae. Alterations of model parameters were done to investigate the circulatory response to rotary blood pump assistance under heart failure conditions. The present model provides a valuable tool for experiment designs, as well as a platform to aid in the development and evaluation of robust physiological pump control algorithms.