Quasi-static Poiseuille flow of antibiotics from an elastomeric pump: Theoretical determination of infusion times and toxicity conditions

We model an elastomeric pump that causes a viscous antibiotic fluid to flow from a pressurized, elastic, spherical reservoir through a horizontally oriented, cylindrical tube to a blood vessel. This flow, under the right conditions, becomes steady state, axially symmetric, Poiseuille flow. As a result, we can determine the length of time for the antibiotic fluid to infuse in terms of the physical properties of the fluid, of the elastomeric ball, of the tube, and of the blood vessel into which the antibiotic infuses. We also obtain a condition that signals toxicity effects and suggest a design that minimizes or eliminates this effect. This analysis is consistent with earlier experimental investigations into the flows of antibiotics from elastomeric pumps.