Analytical method for calculation of deviations from intended dosages during multi-infusion

Abstract

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.

Quantitative assessment of required separator fluid volume in multi-infusion settings

“…This finding may also be explained by Poiseuille flow, which describes the flow through a cylindrical tube where the cross-section of the tube can be divided into laminae (circular layers of fluid). 19 , 20 Each lamina has its own velocity. The outer lamina will have a lower velocity than the middle lamina due to friction with the tubing wall.…”

Infusion Profiler: an Architecture for Generation of Operational Profiles for Intravenous Infusions

“…The second research area explores the pharmacokinetic and pharmacodynamic models of drugs to control intravenous infusion dosages. In this line of research, we highlight the following related works that employ the models of drug absorption by intravenous routes: (i) development of a treatment-controlled infusion system model, which according to its target, explore concepts of mathematically manipulated pharmacokinetics able to consider the particular characteristics of patients resulting in specific parameters Bressan et al (2009); (ii) analyzing the pharmacokinetic employed to study the time dependence of the administered medicines in the definition of the absorption, distribution, metabolism, and excretion of a given drug, thus allowing the configuration modeling of infusion pump operations Trzaska (2014); (iii) enabling predictability in a wide range of possible situations involving many variables and dependencies, which provides the healthcare professional with an accurate prediction of dosing errors and interactive delay times for many scenarios Konings et al (2017) Although there are several works in the literature on these two fronts of research, there are studies that report many factors which may compromise these automation methods. For example, the patient's physiological and pathological characteristics and pharmacological drug factors may negatively influence the control and monitoring actions of infusion system operations Eusuf and Thomas (2019).…”

Drug Flow Through Clinical Infusion Systems: How Modeling of the Common-volume Helps Explain Clinical Events

“…Benchtop (in vitro) modeling of initiating a drug infusion or changing the dose rate of an ongoing infusion shows that there can be a significant lag for the new concentration at the upstream side of the commonvolume to propagate to the patient and achieve the intended steady state delivery. This lag time can lead to delays in intended dose delivery that, under some conditions, can be surprisingly long [12,18,20,21,23]. For infusions into standard central venous catheters of sizeable dead-volume (9 Fr introducer sheath, dead volume~3.2 ml) with inert carrier flow rates designed to minimize excessive fluid administration (10 ml/hr), steady-state drug delivery rates may not be fully realized for over 20 min [18].…”

“…However, in reality there is much complexity in the nuances of drug infusion. Problems in drug dosing can come from startup delays of syringe pumps [3,4], errors in device calibration [9,10], and the complex interaction between multiple infusion devices with different compliances and flow rates through syringes of different barrel sizes leading to potential transient backflow [12,13]. Each of these can result in drug administration that deviates from the user's intent.…”

“…There are many reasons why drug infusion devices may not deliver drug as intended, including but not limited to startup delays within electromechanical systems [3,4], delayed occlusion alarms from slack mechanical components [5][6][7], programming errors [8], inaccuracies in electromechanical drive mechanisms especially at low flow [9,10], decreasing driving pressures within gravity driven systems as crystalloid bags empty [11], and transient reflux of one drug into another syringe line when a catheter is obstructed [12] or one of multiple drugs are transiently stopped for syringe replacements [12,13].…”