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Difficulty: MediumPharmacokinetic and Pharmacodynamic Principles

An infectious disease specialist is consulting on a 48-year-old male inpatient with a severe systemic infection. The patient's body mass is 75 kg75 \text{ kg}. The physician decides to start a continuous intravenous infusion of a narrow-therapeutic-index antibiotic. The established target steady-state serum concentration is 15 mg/L15 \text{ mg/L}. Pharmacokinetic data for this drug indicate a volume of distribution of 0.8 L/kg0.8 \text{ L/kg} and an elimination half-life of 13.86 hours13.86 \text{ hours}. Assuming first-order elimination kinetics, what maintenance infusion rate (in mg/hr\text{mg/hr}) is required to sustain the target concentration?

Answer: 45 mg/hr

Answer

The required maintenance infusion rate is 45 mg/hr45 \text{ mg/hr}.
For a continuous intravenous infusion, the amount of drug entering the body must perfectly match the amount of drug being eliminated in order to maintain a specific steady-state concentration (CssC_{ss}). The elimination rate of a drug is defined by its clearance (CLCL). Thus, the Maintenance Infusion Rate is calculated as CL×CssCL \times C_{ss}. To find CLCL, both the elimination rate constant (kek_e) and the absolute volume of distribution (VdV_d) are required. VdV_d is calculated by multiplying the given 0.8 L/kg0.8 \text{ L/kg} by the patient's 75 kg75 \text{ kg} body weight, yielding 60 L60 \text{ L}. The constant kek_e is derived from the half-life (t1/2t_{1/2}) using the formula ke=0.693t1/2k_e = \frac{0.693}{t_{1/2}}, giving 0.05 hr−10.05 \text{ hr}^{-1}. Consequently, CL=Vd×ke=60 L×0.05 hr−1=3.0 L/hrCL = V_d \times k_e = 60 \text{ L} \times 0.05 \text{ hr}^{-1} = 3.0 \text{ L/hr}. Multiplying this clearance by the target CssC_{ss} of 15 mg/L15 \text{ mg/L} provides the correct maintenance infusion rate of 45 mg/hr45 \text{ mg/hr}.

Step-by-Step Solution

1
Calculate the total volume of distribution (VdV_d) for the patient.
Vd=60 LV_d = 60 \text{ L}
The weight-based parameter (0.8 L/kg0.8 \text{ L/kg}) must be multiplied by the patient's total body weight (75 kg75 \text{ kg}) to find the absolute volume of distribution.
2
Calculate the elimination rate constant (kek_e).
ke=0.05 hr−1k_e = 0.05 \text{ hr}^{-1}
The elimination rate constant is inversely proportional to the half-life, calculated using the standard formula ke=0.693t1/2k_e = \frac{0.693}{t_{1/2}}.
3
Calculate the drug clearance (CLCL).
CL=3.0 L/hrCL = 3.0 \text{ L/hr}
Clearance represents the volume of plasma entirely cleared of the drug per unit time, which is the product of VdV_d and kek_e (CL=Vd×keCL = V_d \times k_e).
4
Calculate the maintenance infusion rate.
45 mg/hr45 \text{ mg/hr}
To maintain a steady-state, the rate of drug administration must equal the rate of elimination. Therefore, Infusion Rate = Clearance ×\times Target Steady-State Concentration (CssC_{ss}).

Key Concept

Calculation of continuous infusion maintenance dosing using clearance and steady-state concentration goals.
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Topics

Pharmacokinetic and Pharmacodynamic Principles

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