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

Area of Science:

• Biomedical Engineering
• Fluid Dynamics
• Pharmacokinetics

Background:

• Multi-infusion setups can lead to dosing errors due to complex fluid dynamics and mechanical interactions.
• Existing numerical methods for calculating these errors are often time-consuming and lack explicit mathematical dependencies.
• Understanding and quantifying these errors is crucial for accurate drug delivery.

Purpose of the Study:

• To develop a novel mathematical framework for calculating dosing errors in multi-infusion systems.
• To integrate mechanical compliance, Poiseuille flow, and dead volume effects into a unified model.
• To generate explicit mathematical expressions for dosing errors, revealing dependencies on hardware parameters and pump settings.

Main Methods:

• Utilized the Z-transform to model catheter contents.
• Implemented the model in Mathematica to automatically generate explicit analytical expressions.
• Validated the theoretical results through three types of in-vitro measurements.

Main Results:

• The new method clearly illustrates the contribution of various factors (e.g., Poiseuille flow, catheter resistance/volume, syringe compliance, pump settings) to dosing errors.
• In-vitro experiments demonstrated good agreement with theoretical predictions, showing a standard deviation of 14% for delay time and 13% for dosing error duration.

Conclusions:

• The developed method provides significant insight and predictability for complex multi-infusion scenarios.
• It enables the potential development of a rapid, bedside tool for interactive prediction of dosing errors and delay times.
• Explicit expressions facilitate real-time calculations, overcoming limitations of conventional numerical simulations.