TITLE:
Quasi-Static, Poiseuille Flow of Analgesics from an Elastomeric Pump: Theoretical Determination of Infusion Times and Toxicity Conditions
AUTHORS:
Clare B. Lipscombe, Trevor C. Lipscombe, Don S. Lemons
KEYWORDS:
Elastomeric Pump, Infusion Therapy, Bio-Fluids, Medical Devices, Antibiotic Delivery, Analgesic Delivery
JOURNAL NAME:
Journal of Biosciences and Medicines,
Vol.12 No.9,
September
26,
2024
ABSTRACT: Background: Elastomeric pumps (elastic balls into which analgesics or antibiotics can be inserted) push medicines through a catheter to a nerve or blood vessel. Since elastomeric pumps are small and need no power source, they fit easily into a pocket during infusion, allowing patient mobility. Elastomeric pumps are widely used and widely studied experimentally, but they have well-known problems, such as maintaining reliable flow rates and avoiding toxicity or other peak-and-trough effects. Objectives: Our research objective is to develop a realistic theoretical model of an elastomeric pump, analyze its flow rates, determine its toxicity conditions, and otherwise improve its operation. We believe this is the first such theoretical model of an elastomeric pump consisting of an elastic, medicine-filled ball attached to a horizontal catheter. Method: Our method is to model the system as a quasi-Poiseuille flow driven by the pressure drop generated by the elastic sphere. We construct an engineering model of the pressure exerted by an elastic sphere and match it to a solution of the one-dimensional radial Navier-Stokes equation that describes flow through a horizontal, cylindrical tube. Results: Our results are that the model accurately reproduces flow rates obtained in clinical studies. We also discover that the flow rate has an unavoidable maximum, which we call the “toxicity bump”, when the radius of the sphere approaches its terminal, unstretched value—an effect that has been observed experimentally. Conclusions: We conclude that by choosing the properties of an elastomeric pump, the toxicity bump can be restricted to less than 10% of the earlier, relatively constant flow rate. Our model also produces a relation between the length of time that the analgesic fluid infuses and the physical properties of the fluid, of the elastomeric sphere and the tube, and of the blood vessel into which the analgesic infuses. From these, we conclude that elastomeric pumps can be designed, using our simple model, to control infusion times while avoiding toxicity effects.