Zero- and First-Order Processes. Individual consumption of oxygen and production of carbon dioxide occur at a constant rate. The rate of change (dx/dt) for a zero-order process

Physiologic Pharmacokinetic Models. If the goal is to determine how to give drugs in order to obtain therapeutic plasma drug concentrations, then all that is needed is to mathematically relate dose to plasma concentration. For this purpose, compartment models are usually adequate.

1. Compartmental Pharmacokinetic Models

   1. The “one compartment model” contains a single volume and a single clearance (Fig. 2-8A).

   2. For anesthetic drugs, the model resemble several buckets connected by pipes (two or three compartment models) (Fig. 2-8B,C).

   3. The sum of the all volumes is the volume of distribution at steady state (Vd_ss).

   4. The clearance leaving the central compartment for the outside is the “systemic” clearance, and the clearances between the central compartment and the peripheral compartments are the “intercompartmental” clearances.

   5. Other than clearance, none of the parameters of compartment models readily translates into any anatomic structure or physiologic process (Fig. 2-9A,B).

2. When drugs are given intravenously, every molecule reaches the systemic circulation (when given by other routes, the drug must first reach the systemic circulation).

3. The plasma concentrations over time following an intravenous bolus resemble the curve in Figure 2-10. This curve has the characteristics common to most drugs when given by intravenous bolus (concentrations continuously decrease over time and the rate of decline is initially steep but becomes less steep over time).

4. Many anesthetic drugs appear to have three distinct phases (Fig. 2-10).

   1. There is a “rapid distribution” phase that begins immediately after bolus injection. Very rapid movement of the drug from the plasma to the rapidly equilibrating tissues characterizes this phase.

   2. Often, there is a second “slow distribution” phase that is characterized by movement of drug into more slowly equilibrating tissues and return of drug to the plasma from the most rapidly equilibrating tissues.

   3. The distinguishing characteristic of the terminal elimination phase is that the plasma concentration is lower than the tissue concentrations, and the relative proportion of drug in the plasma and peripheral volumes of distribution remains constant. During this “terminal phase,” drug returns from the rapid and slow distribution volumes to the plasma and is permanently removed from plasma by metabolism or excretion.

The Time Course of Drug Effect. The plasma is not the site of drug effect for anesthetic drugs. There is a time lag between plasma drug concentration and effect-site drug concentration (Figs. 2-11 to 2-13).

Dose Calculations

1. Bolus Dosing. Conventional approaches to calculate a bolus dose are designed to produce a specific plasma concentration. This makes little sense because the plasma is not the site of drug effect. By knowing the k_e0 (the rate constant for elimination of drug from the effect site) of an intravenous anesthetic, one can design a dosing regimen that yields the desired concentration at the site of drug effect (avoids an overdose) (Table 2-2).

2. Maintenance Infusion Rate. The best approach is through the use of target-controlled drug delivery. With target-controlled drug delivery, the user sets the desired plasma or effect-site concentration. Based on the drug’s pharmacokinetics and the mathematical relationship between patient covariates (weight, age, gender) and individual pharmacokinetic parameters, the computer calculates the dose of drug necessary to rapidly achieve and then maintain any desired concentration (Fig. 2-14).

3. Context-sensitive half-time is the time for the plasma concentration to decrease by 50% from an infusion that maintains a constant concentration. The context-sensitive half-time increases with longer infusion durations because it takes longer for the concentrations to fall if drug has accumulated in peripheral tissues (Figs. 2-15 and 2-16). Context-sensitive half-time and effect-site decrement times are more useful than elimination half-time in characterizing the clinical responses to drugs.