A 62-year-old man is admitted to the pulmonary care unit for management of a severe, refra… — USMLE Step 3

A 62-year-old man is admitted to the pulmonary care unit for management of a severe, refractory asthma exacerbation. The medical team initiates a continuous intravenous infusion of an adjunctive bronchodilator at a rate of $40 \text{ mg/hr}$ . The medication exhibits first-order elimination kinetics. For this specific patient, the drug has a volume of distribution ( $V_d$ ) of $40 \text{ L}$ and an elimination half-life ( $t_{1/2}$ ) of $6.93 \text{ hours}$ (note: $\ln(2) \approx 0.693$ ). To rapidly achieve therapeutic levels, the physician orders an initial intravenous loading dose designed to immediately establish the exact steady-state plasma concentration that the continuous infusion will eventually maintain.

What is the required loading dose of the medication in milligrams?

Cevap: 400 mg

Cevap

400

To achieve the eventual steady-state concentration immediately, the administered loading dose must fill the patient's volume of distribution to that specific target concentration. First, find the target steady-state concentration (

C_{ss}

) that the infusion will achieve, which is defined as

C_{ss} = \frac{\text{Infusion Rate}}{Cl}

. The clearance (

Cl

) is found using

Cl = k_e \times V_d

, where

k_e = \frac{0.693}{t_{1/2}}

. For this patient,

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

, and

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

. Consequently,

C_{ss} = \frac{40 \text{ mg/hr}}{4 \text{ L/hr}} = 10 \text{ mg/L}

. The loading dose required is

LD = C_{ss} \times V_d = 10 \text{ mg/L} \times 40 \text{ L} = 400 \text{ mg}

. Alternatively, this calculation algebraically simplifies to

LD = \frac{\text{Infusion Rate}}{k_e} = \frac{40}{0.1} = 400 \text{ mg}

Adım Adım Çözüm

Calculate the elimination rate constant (

k_e

k_e = 0.1 \text{ hr}^{-1}

The elimination rate constant is inversely proportional to the half-life:

k_e = \frac{0.693}{t_{1/2}} = \frac{0.693}{6.93 \text{ hr}}

Calculate the drug clearance (

Cl

Cl = 4 \text{ L/hr}

Clearance is the product of the elimination rate constant and the volume of distribution:

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

Calculate the target steady-state plasma concentration (

C_{ss}

C_{ss} = 10 \text{ mg/L}

At steady state, the continuous infusion rate equals the elimination rate.

C_{ss} = \frac{\text{Infusion Rate}}{Cl} = \frac{40 \text{ mg/hr}}{4 \text{ L/hr}}

Calculate the required loading dose (

LD

LD = 400 \text{ mg}

The loading dose required to achieve a specific target concentration immediately is the product of that target concentration and the volume of distribution:

LD = C_{ss} \times V_d = 10 \text{ mg/L} \times 40 \text{ L}

Anahtar Kavram

Calculating a loading dose designed to immediately achieve the steady-state concentration of a planned continuous infusion.

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