20 40 60 80 100120140 Time
Figure 1.4 Alteration of MEC in a state-varying system.

parameters (bottom panel). In both plots, the solid line is the drug-con-centration-versus-time profile in response to a zero-order input, and the dotted and dashed lines represent the MEC and MTC, respectively. The bottom panel could represent the presence of pharmacodynamic drug tolerance (e.g., receptor desensitization). In the bottom panel, the drug starts out effective, and then, as drug tolerance develops, Cp is no longer greater than MEC, resulting in drug ineffectiveness.

1.5 Pharmacokinetics: Input, Disposition, and Convolution

In linear pharmacokinetics, the drug concentration-versus-time-course profile is the result of two distinct kinetic components—input and disposition. Nearly all dosage forms, both old and new, can be classified into one of three kinetic categories—instantaneous, zero order, or first order. Since the physiology, anatomy, and drug physicochemical characteristics largely determine the disposition component, if we want to have any control over the drug's concentration profile, we must modulate the input. The next subsection identifies the kinetic order of the most commonly used dosing inputs, followed by a subsection on the kinetic order of different disposition models and a concluding subsection describing the mathematical combination of an input function and disposition function to give a complete drug concentration kinetic profile.

1.5.1 Input

The regulation of drug input into the body is the core tenet of controlled release drug delivery systems. With advances in engineering and material sciences, controlled release delivery systems are able to mimic multiple kinetic types of input, ranging from instantaneous to complex kinetic order. In this section three of the most common input functions found in controlled release drug delivery systems will be discussed— instantaneous, zero order, and first order.

Instantaneous input (IB). Truly instantaneous input (IB) does not physically exist; in fact, the kinetic order is mathematically undefined. However, when the input kinetics are exceedingly fast compared with distribution and elimination kinetics, the dose provides a relatively "instantaneous" input. The best example of an "instantaneous" input is an intravenous bolus dose—where the drug is administered over a short period (<5 minutes) and directly into the systemic circulation. Figure 1.5 (left panel) shows this type of input being given at time = t'. When the intravenous bolus is given repetitively at a fixed interval

Instantaneous input (e.g., i.v. bolus) 100 "i 90 -80 -70 -60 -50 -40 -30 -20 -10 0

t Time

0 0

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