TY - JOUR
T1 - Analytical method for calculation of deviations from intended dosages during multi-infusion
AU - Konings, Maurits K.
AU - Snijder, Roland A.
AU - Radermacher, Joris H.
AU - Timmerman, Annemoon M.
N1 - Funding Information:
This research was partly funded by the EMRP project Metrology for drug delivery. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union.
Funding Information:
This research was partly funded by the EMRP project Metrology for drug delivery. The EMRP has not been involved in the design of this particular study, and has not been involved in writing the manuscript, or in the collection, analysis, interpretation of the data.
Publisher Copyright:
© 2017 The Author(s).
PY - 2017/1/17
Y1 - 2017/1/17
N2 - Background: In 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. Methods: Our 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. Results: The 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. Conclusions: Our 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.
AB - Background: In 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. Methods: Our 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. Results: The 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. Conclusions: Our 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.
KW - Catheter
KW - Dosing error
KW - Infusion
KW - Mathematical model
KW - Poiseuille flow
KW - Safety
UR - http://www.scopus.com/inward/record.url?scp=85011340514&partnerID=8YFLogxK
U2 - 10.1186/s12938-016-0309-4
DO - 10.1186/s12938-016-0309-4
M3 - Article
C2 - 28095851
AN - SCOPUS:85011340514
SN - 1475-925X
VL - 16
JO - BioMedical Engineering Online
JF - BioMedical Engineering Online
IS - 1
M1 - 18
ER -