A pumping system for use in medical applications where liquids must be infused and aspirated from a mammalian patient, and whose economics are such that it is cost effective to simply dispose of it after a single use. The system features positive displacement pump(s) such as reciprocating pump(s) containing a damping mechanism to dampen out the peaks and valleys in the fluid pressure that is pumped, which is important for preventing cavitation. The system furthermore features a shut-off valve on the extraction side so that certain injected fluids such as contrast medium, are not immediately pumped out of the patient. In a preferred embodiment, the system also features means for independently controlling the fluid pressure/volume on the infusion and extraction sides, self-priming capability, a continuous fluid path, and visual air bubble detection, with viewports located at important points in the fluid path, such as at pumps and valves.