A 45-year-old man weighing 80 \text{ kg} is admitted to the hospital with a severe skin an… — USMLE Step 3

A 45-year-old man weighing $80 \text{ kg}$ is admitted to the hospital with a severe skin and soft tissue infection. The physician decides to initiate therapy with a novel oral antimicrobial agent. To ensure immediate therapeutic effect, a loading dose is required. The target peak plasma concentration for this medication is $15 \text{ mg/L}$ . The drug has a known volume of distribution of $0.6 \text{ L/kg}$ and an oral bioavailability of $75\%$ .

What is the required oral loading dose in mg to achieve the desired peak plasma concentration?

Answer: 960 mg

Answer

960

The required oral loading dose is found by first determining the total volume of distribution (

0.6 \text{ L/kg} \times 80 \text{ kg} = 48 \text{ L}

). Next, this volume is multiplied by the target peak concentration (

15 \text{ mg/L}

) to find the required systemic drug amount (

720 \text{ mg}

). Finally, dividing by the oral bioavailability fraction (

0.75

) accounts for incomplete absorption and first-pass metabolism, yielding a final loading dose of

960 \text{ mg}

Step-by-Step Solution

Calculate the total volume of distribution (

V_d

) for the patient.

V_d = 0.6 \text{ L/kg} \times 80 \text{ kg} = 48 \text{ L}

The volume of distribution is provided per kilogram of body weight, so it must be scaled to the patient's actual weight.

Calculate the total amount of drug required in the systemic circulation.

\text{Amount} = 48 \text{ L} \times 15 \text{ mg/L} = 720 \text{ mg}

The total amount of drug needed in the body is the product of the target peak concentration and the total volume of distribution.

Adjust for the drug's oral bioavailability (

F

) to find the required oral loading dose.

\text{Oral Loading Dose} = \frac{720 \text{ mg}}{0.75} = 960 \text{ mg}

Since only

75\%

of the orally administered dose reaches the systemic circulation, the calculated IV equivalent dose must be divided by the bioavailability fraction.

Key Concept

The oral loading dose is calculated using the formula:

\text{Loading Dose} = \frac{V_d \times \text{Target Concentration}}{F}

, taking care to calculate the total

V_d

based on patient weight.

Alternative Method

The calculation can be performed in a single combined formula:

\text{Loading Dose} = \frac{V_d \times \text{Weight} \times \text{Target Concentration}}{F} = \frac{0.6 \times 80 \times 15}{0.75} = 960 \text{ mg}

Estimated Time:1m 30s

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