A 55-year-old female patient is hospitalized for the management of severe pneumonia compli… — USMLE Step 3

A 55-year-old female patient is hospitalized for the management of severe pneumonia complicated by sepsis. Her current body weight is $80 \text{ kg}$ . The medical team decides to initiate therapy with an intravenous antimicrobial agent. This medication has a volume of distribution ( $V_d$ ) of $0.5 \text{ L/kg}$ and follows first-order elimination kinetics with a half-life ( $t_{1/2}$ ) of $6.93 \text{ hours}$ . The drug is prescribed to be administered intermittently as an intravenous infusion every $12 \text{ hours}$ . To achieve optimal bactericidal activity, the target average steady-state plasma concentration ( $C_{ss,avg}$ ) is $10 \text{ mg/L}$ . Assuming $100\%$ bioavailability for the intravenous route, what maintenance dose should be administered every $12 \text{ hours}$ ?

Answer: 480 mg

Answer

480

The maintenance dose (

MD

) is the amount of drug required to replace what is eliminated over a dosing interval (

\tau

) to maintain a target average steady-state concentration (

C_{ss,avg}

). The formula is

MD = \frac{C_{ss,avg} \times CL \times \tau}{F}

. First, clearance (

CL

) must be determined. Clearance is the product of the elimination rate constant (

k_e

) and the volume of distribution (

V_d

). The patient's total

V_d

0.5 \text{ L/kg} \times 80 \text{ kg} = 40 \text{ L}

. The elimination rate constant is

k_e = \frac{0.693}{t_{1/2}} = \frac{0.693}{6.93 \text{ hours}} = 0.1 \text{ hr}^{-1}

. Therefore,

CL = 0.1 \text{ hr}^{-1} \times 40 \text{ L} = 4 \text{ L/hr}

. For an intravenous drug (

F = 1

), the maintenance dose administered every

12 \text{ hours}

MD = 10 \text{ mg/L} \times 4 \text{ L/hr} \times 12 \text{ hours} = 480 \text{ mg}

Step-by-Step Solution

Calculate the patient's total volume of distribution (

V_d

V_d = 0.5 \text{ L/kg} \times 80 \text{ kg} = 40 \text{ L}

Total volume of distribution is required to calculate the total body clearance of the drug.

Calculate the elimination rate constant (

k_e

) and total body clearance (

CL

k_e = \frac{0.693}{6.93 \text{ hr}} = 0.1 \text{ hr}^{-1}

. Clearance (

CL

) =

k_e \times V_d = 0.1 \text{ hr}^{-1} \times 40 \text{ L} = 4 \text{ L/hr}

Clearance determines the rate at which the drug must be replaced to maintain steady-state concentrations.

Calculate the maintenance dose (

MD

) for the specified dosing interval.

MD = C_{ss,avg} \times CL \times \tau = 10 \text{ mg/L} \times 4 \text{ L/hr} \times 12 \text{ hr} = 480 \text{ mg}

The maintenance dose replaces the amount of drug cleared over one dosing interval (

\tau

) to maintain the target steady-state concentration.

Key Concept

Calculation of maintenance dose requires determining clearance from half-life and volume of distribution, then multiplying by the target steady-state concentration and dosing interval.

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