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V1 most likely would be used when calculating a loading dose for a drug exhibiting two-compartment behavior. V2 is almost never used in the determination of dosing but sometimes may be used in blood protein or tissue-binding calculations and in the estimation of Vd,ss.

Vd,extrap (volume of distribution, extrapolated). Vd,extrap is given by V - dosei.v. bolus - V (a - P)

Although Vd,extrap is the same as Vd from the one-compartment disposition model, one should apply this volume term cautiously to systems greater than one compartment. As Eq. (1.37) shows, Vd,extrap is dependent on the elimination rate from the central compartment (k10) in a complex interaction between a and p. Of all the volume terms, Vd,extrap overestimates the volume to the greatest degree and is probably the least useful in the design of controlled release delivery systems.

Vd,area or Vd,p (volume of distribution, area or P). Vdarea is given by Eq. (1.38):

V - V - dosei v. bolus d,area - d,p- (AUC)(P) (1.38)

This volume term also depends on b and/or k10 and overestimates the volume. However, when terminal concentration-time data are used (i.e., distribution is at steady state and elimination is the process significantly altering Cp), this volume term will produce an accurate conversion factor between Cp and the amount of drug in the body. While Vd area overestimates the volume, it can be useful in the design of controlled release delivery systems, particularly in pulsatile delivery.

Vd,ss (volume of distribution, steady state). This volume term and Vdarea, are probably the two most useful in appropriate dose determination. Vdss is used in calculating maintenance doses for an individual whose drug concentration is at steady state. Unlike Vdarea, Vdss does not change with changes in elimination (i.e., a, P, or k10 does not show up in Vdss):

Generally, since the goal of some controlled release delivery systems is to achieve and maintain the drug at a steady-state concentration within the therapeutic window, Vdss is used frequently to determine the dose that will achieve this therapeutic target.

Cl, AUC, t1/2,a, f1/2 p- Assuming that A, B, a, and b have been obtained either graphically or from a nonlinear regression software package, for a two-compartment disposition model, the equations for Cl, AUC, tl/2, a, and tl/2, P are given in Eqs. (1.40) through (1.42):

1.6.2 Multiple-dosing input systems and steady-state kinetics.

Since the goal of most controlled release delivery systems is to maintain the drug concentration within the therapeutic window, the effect of multiple-dosing strategies (used in chronic diseases) on Cp will be discussed. In this section we assume that the blood/plasma drug concentration achieves its steady state rapidly with all involved tissues, especially the concentration at site of effect Ce or biophase concentration. The MEC and MTC are determined by Ce. If Cp and Ce are in a steady-state relationship or rapidly reach a steady-state relationship, then controlling Cp should effectively control Ce and presumably the response generated by Ce. This relationship between Cp and Ce is one of the foundational assumptions of using pharmacokinetics in the design of most controlled release delivery devices.

Zero-order input and one-compartment disposition (I0D1). The simplest case for achieving a drug plasma concentration between the MEC and MTC is to use a zero-order input. In Fig. 1.17, the six time points show time as measured in half-lives. At 3.3 half-lives, Cp is at approximately 90 percent of its true steady-state value; at 5 half-lives, Cp is at approximately 96 percent of its true steady-state value.

Multiple instantaneous input and one-compartment disposition (IBD1). In the case of IBD1 single-dose input, the Cp kinetic profile is given by Eq. (1.43) for any time t after the bolus dose has been given:

Time

Figure 1.17 Cp versus time profile for zero-order input and one-compartment disposition.

Time

Figure 1.17 Cp versus time profile for zero-order input and one-compartment disposition.

dose

If drug had been administered in equally sized multiple intravenous bolus doses at equally spaced t time intervals (e.g., t = 6 h), then an accounting of accumulated drug between doses must be instituted. Figure 1.18, similar to the zero-order input, shows that repetitive instantaneous dosing will produce an average Cp profile similar to Fig. 1.17. For multiple intravenous bolus doses, Cp in the nth dosing period is

MDF is the multiple dosing factor and is defined in Eq. (1.45):

As Schoenwald28 points out, the MDF is quite mobile in its application and can be applied to obtain two important concentrations in the design of controlled release delivery systems—Cp max and Cp,min. Under multiple-dosing intravenous bolus input, applying MDF to Cp max and CPmmin gives Eqs. (1.46) and (1.47):

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