The study of the interaction between a pneumatic left ventricle assist device (LVAD), driven with different control strategies, and the cardiovascular system is the subject of this paper. It is performed by a modular numerical model of the cardiovascular system connected to a numerical model of the LVAD. The circulatory system is simulated by a lumped parameter numerical model. The ventricle is represented by a time-varying elastance model to reproduce the Starling law of the heart. The effect of the LVAD on the cardiovascular system is evaluated, on the left ventricle alone, by an open-loop circuit consisting of the models of the ventricle, the LVAD and the arterial tree. The analysis is performed in terms of energy variables (such as external work and oxygen consumption and cardiac mechanical efficiency versus control strategy. The LVAD is driven by different control strategies: a fixed heart rate (with different delays from the onset of the natural ventricle contraction) and a variable heart rate.