With respect to rotary blood pumps used as left ventricular assist devices (LVADs), it is clinically important to control pump flow to avoid complications associated with over-or under-pumping of the native heart. By employing only the non-invasive observer of instantaneous pump impeller speed to assess flow dynamics, a number of physiologically significant pumping states may be detected. Based on a number of acute animal experiments, five such states were identified: regurgitant pump flow (PR), ventricular ejection (VE), non-opening of the aortic valve (ANO), and partial collapse (intermittent and continuous) of the ventricle wall (PVC-I and PVC-C). Two broader states, normal (corresponding to VE, ANO) and suction (corresponding to PVC-I, PVC-C) were readily discernable in clinical data from human patients implanted with LVADs. Based on data from both the animal experiments (N=6) and the human patients (N=10), a strategy for the automated non-invasive detection of significant pumping states has been developed and validated. Employing a classification and regression tree (CART), this system detects pumping states with a high degree of accuracy: state VE -87.5/100.0% (sensitivity/specificity); state ANO - 98.1/92.5%; state PVC-I - 90.0/90.2%; state PVC-C - 61.2/98.0%. With a simplified binary scheme differentiating suction and normal states, both states were detected without error in data from the animal experiments, and with a sensitivity/specificity, for detecting suction, of 99.2/98.3% in the human patient data.