Calculator for Estimating Drainage Flow Rate

How It Works

This calculator accepts inputs for catheter size, length, and viscosity, and outputs the calculated flow rate. If desired, a flow rate can be inputted as well to calculate the required catheter diameter to achieve that flow rate.

Background

This tool was built by Audrey Shih and is intended for physicians performing abscess drainage procedures. It predicts the flow rate of a fluid through a catheter, given the zero-shear viscosity, \( \eta_0 \) measured by the magnetic stress rheometer (MSR). The calculations are based on the following equation:

In the formula above, Q is the predicted flow rate, \( \eta_0 \) is the zero-shear viscosity, \( \Delta P \) is the gauge pressure inside the abscess, R is the catheter radius, and L is the length of the catheter.

This equation was derived by Audrey Shih, Omkar Shende, and the Fuller Group at Stanford University. Based on our rheological modeling of abscess fluid samples, we have found that this equation is sufficient to describe flow rates during abscess fluid drainage. The study detailing this analysis has been published in Physics of Fluids.

Model Assumptions

• Constant pressure drop. We use a nominal intracystic pressure for \( \Delta P \) of ~15 mm Hg or 2000 Pa.
• Constant viscosity \( \eta_0 \) with negligible viscoelastic effects. Based on our work, we find that viscoelastic effects are typically negligible. Any viscoelastic effects that manifest would result in a higher flow rate than estimated, not lower.
• Catheter radii R lengths L based on Cook Medical multipurpose drainage catheters. The same French sizing of a different brand may be a different inner diameter.
• No stopcocks or other obstructions in the catheter.

Flow Rate and Catheter Size Calculator