A system for pumping blood to assist or assume the cardiac function of a patient is characterized by a blood pump that exhibits a steep performance curve such that only small changes in pump flow occur for large changes in differential pressure across the pump. The pump therefore exhibits flow-limiting characteristics to protect the physiological system against harmful flow rates or pressures. Pump flow may also be limited by controlling the current provided to a driver from a power supply or by suitable restrictions within or external to the pump housing.