Cheng Prusoff Equation Calculator

How to Use the Calculator

1. Enter the elimination rate constant (ke) in units of h⁻¹. This represents how quickly the drug is eliminated from the body.
2. Enter the zero-order input rate (k₀) in units of mg/h. This represents the constant amount of drug being administered per hour.
3. Click the "Calculate" button to compute the steady-state concentration (Css).
4. The result will be displayed in units of mg/L, representing the concentration of the drug in the blood at steady state.

Understanding the Cheng Prusoff Equation

The Cheng Prusoff equation is a simplified model for calculating steady-state drug concentrations when only elimination rate constants are available:

Css = k₀ / ke

Where:

• Css = Steady-state concentration (mg/L)
• k₀ = Zero-order input rate (mg/h) - This is the constant amount of drug administered per hour.
• ke = Elimination rate constant (h⁻¹) - This represents how quickly the drug is eliminated from the body.

Example

If a drug has an elimination rate constant of 0.1 h⁻¹ and is administered at a rate of 50 mg/h, the steady-state concentration would be:

Css = 50 mg/h / 0.1 h⁻¹ = 500 mg/L

Applications

This calculator is useful in pharmacokinetics for:

• Estimating steady-state drug concentrations when only elimination parameters are known.
• Comparing different dosing regimens to achieve target steady-state concentrations.
• Understanding how changes in elimination rate affect steady-state concentrations.

Limitations

The Cheng Prusoff equation assumes that absorption follows zero-order kinetics and that elimination follows first-order kinetics. In reality, many drugs follow more complex absorption and elimination patterns. This calculator provides a simplified model that may not be accurate for all drugs.