Mathematical and physical model of gravity-fed infusion outflow: application to soft-bag-packed solutions

Gravity-fed infusion (GFI) systems are acknowledged as being unable to keep their flow-rate constant. This may affect drug plasma levels such as aminoglycosides. Numerous factors have previously been cited, but their relative importance has never been quantified so far. The objective of this work is to identify the main factors that influence GFI in vitro outflow and to propose a mathematical model of flow-rate evolution as a function of time. In this model, pressure loss and infusion device creep have been considered as the main variation factors. Concomitantly, two experiments were undertaken. Firstly, the flow-rate evolution of an in vitro infusion of 250 mL of dextrose 5% was assessed. Secondly, the creep occurring on an infusion device was measured through a stress relaxation experiment. The experimental infusion flow-rate decreased by as much as 28.5% over 1 h. Simulated and experimental data are well correlated (r = 0.987; P < 0.0001). The maximum creep effect happens during the first 15 min of infusion. In this work, height of the liquid in the bag and tube creep were found to be the main variation factors in GFI flow-rate. This new mathematical model should help to explain the differences observed in drug plasma levels with gravity-fed devices.