# Calculation of Drug Concentration

## Non-Uniform Multiple IV Bolus Dose Regimen

A patient is started on a drug at an IV bolus dose of 50 mg at time zero, 100 mg at 12 hours and 250 mg at 16 hours (makes no sense but a nice random regimen :- all times are from time zero). Calculate the drug concentration at a few of time points during the first three dosing interval. It might be useful if you sketch the expected data or dosing regimen (this sketch is not required for the homework exercise). Specifically calculate the concentration three hours after the first dose, two hours after the second dose and one hour after the third dose.
Assume a one compartment linear model applies to this drug in this concentration range.
The kel and V for this drug in this patient are 0.23 hr^{-1} and 40.8 L, respectively.

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**An equation:**

**Equation 25.4.1** Drug Concentration during a Multiple Dose Regimen (Non-Uniform Regimen)

where t is time since the first dose was given, d2 is the time when the second dose was given (since the first dose) and d3 is the time when the third dose was given (since the first dose). Remember to include two terms (exponential terms) after the second dose, three terms after the third dose, etc., when calculating total concentration after the second, third, and subsequent doses.
See also the section on the Superposition Principle

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