Multi-infusion therapy, in which multiple pumps are connected to one access point, is frequently used in patient treatments. This practice is known to cause dosing errors following setpoint changes in the drug concentrations that actually enter the patients. Within the Metrology for Drug Delivery Project, we analyzed and quantified the two main physical phenomena leading to these errors: the "push-out" effect and the system mechanical compliance. We compared the dosing errors of a three-pump system with two infusion sets, both with and without anti-reflux valves, using in vitro spectrophotometric experiments. Additionally, computer simulations were used to study the compliance effect separately. We found a start-up time of more than 1 h, and a dosing error following a setpoint increase of another pump for the low flow rate pump, corresponding to 0.5 μg noradrenaline delivered in 8 min. We showed that the dead volume inside the tubes and syringe compliance produce opposite deviations from the setpoint values in the actual drug output concentrations, making the net result hard to predict and often counterintuitive. We conclude that metrology on compliance and push-out effects could be used by infusion device manufacturers to successfully improve drug delivery performance and relevant standards for high-risk multi-infusion applications.

BackgroundIn this paper, a new method is presented that combines mechanical compliance effects with Poiseuille flow and push-out effects (“dead volume”) in one single mathematical framework for calculating dosing errors in multi-infusion set-ups. In contrast to existing numerical methods, our method produces explicit expressions that illustrate the mathematical dependencies of the dosing errors on hardware parameters and pump flow rate settings.MethodsOur new approach uses the Z-transform to model the contents of the catheter, and after implementation in Mathematica (Wolfram), explicit expressions are produced automatically. Consistency of the resulting analytical expressions has been examined for limiting cases, and three types of in-vitro measurements have been performed to obtain a first experimental test of the validity of the theoretical results.ResultsThe relative contribution of various factors affecting the dosing errors, such as the Poiseuille flow profile, resistance and internal volume of the catheter, mechanical compliance of the syringes and the various pump flow rate settings, can now be discerned clearly in the structure of the expressions generated by our method. The in-vitro experiments showed a standard deviation between theory and experiment of 14% for the delay time in the catheter, and of 13% for the time duration of the dosing error bolus.ConclusionsOur method provides insight and predictability in a large range of possible situations involving many variables and dependencies, which is potentially very useful for e.g. the development of a fast, bed-side tool (“calculator”) that provides the clinician with a precise prediction of dosing errors and delay times interactively for many scenario’s. The interactive nature of such a device has now been made feasible by the fact that, using our method, explicit expressions are available for these situations, as opposed to conventional time-consuming numerical simulations.