Abstract: An apparatus for infusing TPN fluids to a patient includes a source of fluid, a pump for infusing fluid from the source to the patient, and a computer for controlling the operation of the pump. During the operation of the apparatus the infusion rate of the pump is varied according to an infusion regimen that is based on the volume of fluid to be infused and the time during which the fluid is to be infused. This regimen is characterized by a trifurcated ramp up region having interrelated incremental rates of infusion which transition the pump from a zero rate of infusion to a steady state rate of infusion. The infusion regimen is also characterized by a period of steady state infusion which follows the ramp up region, and a ramp down region in which the infusion rate is decremented from the steady state rate based on the remaining volume of fluid to be infused to the patient and the remaining time for infusing this remaining volume of fluid.