A system and method for transitioning between therapeutic substances to be delivered at different flow rates to a patient. The first therapeutic substance is delivered to the patient at a known flow rate, a bridge duration equal to the known volume divided by the known flow rate is calculated； and the flow rate is controlled following introduction of a second therapeutic substance into the reservoir. If the second flow rate is lower than the first flow rate, delivery is begun of at least one of the first therapeutic substance and the second therapeutic substance at the second flow rate at least as soon as the bridge duration is over. Otherwise, delivery is begun of the at least one of the first therapeutic substance and the second therapeutic substance at the second flow rate at least as late as when the bridge duration is over.
