A blood pump system for persistently increasing the overall diameter and lumen diameter of peripheral veins and arteries by persistently increasing the speed of blood and the wall shear stress in a peripheral vein or artery for a period of time sufficient to result in a persistent increase in the overall diameter and lumen diameter of the vessel is provided. The blood pump system includes a blood pump, blood conduit(s), a control system with optional sensors, and a power source. The pump system is configured to connect to the vascular system in a patient and pump blood at a desired rate and pulsatility. The pumping of blood is monitored and adjusted, as necessary, to maintain the desired elevated blood speed, wall shear stress, and desired pulsatility in the target vessel to optimize the rate and extent of persistent increase in the overall diameter and lumen diameter of the target vessel.