Determination of Multiple Dosing Parameters: Steady-State, Minimum and Maximum Concentrations

Gentamicin, an aminoglycoside antibiotic, is commonly administered via intermittent intravenous infusion to treat severe infections. An intermittent one-hour infusion of gentamicin, administered at eight-hour intervals, allows for precise control of plasma drug concentrations, minimizing toxicity while ensuring therapeutic efficacy. Pharmacokinetic principles govern the dynamics of plasma concentrations and can be mathematically described using specific equations.

The plasma drug concentration after a single infusion is calculated using an equation incorporating the infusion duration t_inf. This initial calculation provides a foundation for understanding the drug's behavior within the body following administration.

At the steady state, the maximum plasma drug concentration, achieved after the nth infusion, is determined by another equation. This incorporates the dosing interval τ, and the accumulation factor 1/(1 - e^-kτ) accounts for the repeated dosing, reflecting the drug's progressive build-up until a stable concentration is reached.

The plasma concentration at any time after the last infusion is derived using an equation that accounts for the exponential decline of the drug's concentration over time. This decline is influenced by the time elapsed since the end of the infusion, enabling precise predictions of plasma levels during the dosing interval.

Lastly, the trough plasma drug concentration at the steady state is determined to assess the minimum concentration before the next dose. This parameter is critical for ensuring plasma levels remain above the minimum inhibitory concentration, reducing the risk of treatment failure.

These calculations elucidate the interplay between infusion rate, clearance, and dosing intervals. By understanding these dynamics, clinicians can make informed adjustments to therapeutic drug monitoring, optimizing gentamicin therapy while minimizing the risk of toxicity.