A 54-year-old man is admitted to the intensive care unit with a severe bloodstream infecti… — USMLE Step 3

A $54$ -year-old man is admitted to the intensive care unit with a severe bloodstream infection caused by *Pseudomonas aeruginosa*. He is to be started on an intravenous aminoglycoside. The patient weighs $80$ kg. His estimated volume of distribution for the drug is $0.25$ L/kg.

To ensure optimal bactericidal activity and minimize the risk of acute tubular necrosis, the clinical pharmacist recommends targeting a steady-state peak serum concentration of $8.0$ mg/L and a steady-state trough serum concentration of $2.0$ mg/L. Based on the patient's current renal function, the elimination half-life of the drug is determined to be $8$ hours.

Assuming the drug follows a one-compartment pharmacokinetic model and distributes instantaneously, what maintenance dose (in mg) must be administered at each dosing interval to achieve these exact steady-state target concentrations?

Answer: 120 mg

Answer

120

In a one-compartment pharmacokinetic model with intermittent IV bolus dosing, steady state is achieved when the amount of drug administered equals the amount eliminated during the dosing interval. Therefore, the change in concentration from the trough (right before the dose) to the peak (immediately after the dose) represents the concentration contribution of a single maintenance dose. This change (

\Delta C

) is calculated as Target Peak - Target Trough (

8.0 - 2.0 = 6.0

mg/L). The required dose is this concentration change multiplied by the volume of distribution (

20

L), which equals

120

mg. This mathematically elegant method bypasses the need to calculate the elimination rate constant (

k

) or the exact dosing interval (

\tau

Step-by-Step Solution

Calculate the patient's total volume of distribution (

V_d

V_d = 80 \text{ kg} \times 0.25 \text{ L/kg} = 20 \text{ L}

The total distribution volume is required to relate the drug amount (dose) to its plasma concentration.

Determine the required change in concentration (

\Delta C

) per dose at steady state.

\Delta C = \text{Peak} - \text{Trough} = 8.0 \text{ mg/L} - 2.0 \text{ mg/L} = 6.0 \text{ mg/L}

At steady state, the concentration added by each administered dose exactly replaces the concentration eliminated during the preceding dosing interval.

Calculate the required maintenance dose.

\text{Dose} = \Delta C \times V_d = 6.0 \text{ mg/L} \times 20 \text{ L} = 120 \text{ mg}

The dose is the product of the required concentration change and the volume of distribution.

Key Concept

At steady state for an intermittently dosed IV bolus, the required maintenance dose is directly proportional to the difference between the steady-state peak and trough concentrations multiplied by the volume of distribution.

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