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where ka is the first-order absorption rate constant (units of 1/time), K is the first-order rate constant of elimination (units of 1/time), Vd is the volume of distribution (units of volume), F is the fraction of the administered dose that is delivered to the systemic circulation as parent compound (no units, varies from 0 to 1), and S is the formulation salt factor (no units, varies from 0 to 1). Vd can be determined by Eq. (1.27):

which is the same equation for Vd(area) in two-compartment disposition models. In one-compartment disposition models, Vd(area) degenerates into Vd. Two other parameters, Cpmax and tmax, which identify the maximum drug concentration reached and the time at which that maximum is reached, respectively, are useful in the design of controlled release delivery systems. These values are calculated by Eqs. (1.28) and (1.29), and the graphic representation of these values can be seen on Fig. 1.14.

Instantaneous input and two-compartment disposition (IBD2). The IBD2

model adds another level of reality and complexity to the IBD1 model yet still remains relevant and computationally accessible to most scientists. The two-compartment model is a nice compromise that allows for distribution and elimination kinetics, whereas one-compartment models only have elimination kinetics. In the IBD2 model, the input is an intravenous bolus dose, and the disposition consists of two compartmentsâ€”a "central" compartment and a "tissue" compartment (Fig. 1.15).

The central compartment represents the blood/plasma and any other tissue that rapidly equilibrates, relative to the distribution rate, with the blood/plasma (e.g., liver or heart tissue). The tissue compartment represents all other tissues that keep the drug and reach steady-state concentrations more slowly than the tissues of the central compartment. Since the two-compartment model is fairly robust in describing a bulk of all drugs, we will limit our discussion to two compartments with elimination

Dose

Compartment 1 (central) CP |
k12 |
Compartment 2 (tissue) |

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