Drugs may be administered to patients by one of various routes including oral, topical, or parenteral routes of administration. Examples of parenteral routes of administration include intravenous, subcutaneous, and intramuscular. Intravenous (IV) drug solutions may be given either as a bolus dose (injected all at once) or infused slowly through a vein into the plasma at a constant or zero-order rate. The main advantage for giving a drug by IV infusion is that IV infusion allows precise control of plasma drug concentrations to fit the individual needs of the patient. For drugs with a narrow therapeutic window (eg, heparin), IV infusion maintains an effective constant plasma drug concentration by eliminating wide fluctuations between the peak (maximum) and trough (minimum) plasma drug concentration. Moreover, the IV infusion of drugs, such as antibiotics, may be given with IV fluids that include electrolytes and nutrients. Furthermore, the duration of drug therapy may be maintained or terminated as needed using IV infusion.
The plasma drug concentration–time curve of a drug given by constant IV infusion is shown in Fig. 5-1. Because no drug was present in the body at zero time, drug level rises from zero drug concentration and gradually becomes constant when a plateau or steady-state drug concentration is reached. At steady state, the rate of drug leaving the body is equal to the rate of drug (infusion rate) entering the body. Therefore, at steady state, the rate of change in the plasma drug concentration dCp/dt = 0, and
Plasma level–time curve for constant IV infusion.
Based on this simple mass balance relationship, a pharmacokinetic equation for infusion may be derived depending on whether the drug follows one- or two-compartment kinetics.
The pharmacokinetics of a drug given by constant IV infusion follows a zero-order input process in which the drug is directly infused into the systemic blood circulation. Equation 5.2 gives the plasma drug concentration at any time during the IV infusion where t is the time for infusion. The graph of Equation 5.2 appears in Fig. 5-1 and 5-2. For most drugs, elimination of drug from the plasma is a first-order process. Therefore, in this one-compartment model, the infused drug follows zero-order input and first-order output. The change in the amount of drug in the body at any time (dDB/dt) during the infusion is the rate of input minus the rate of output.
where DB is the amount of drug in the body, R is the infusion rate (zero order), and k is the elimination rate constant (first order).
Integration of Equation 5.1 and substitution of DB = CpVD gives:
As the drug is infused, the value for time (...