Multicompartment models

Fig. 39.2. Multicompartment model which, in addition to Fig. 39.1, takes into account that the drug is buffered in adipose (fatty) tissue, excreted by the kidneys and metabolized in the liver.

The research published in this book uses the presently most comprehensive multicompartment model, the first which comprises a coupled atmosphere-ocean general circulation model (GCM). GCMs are the state-of-the-art tools used in climate research. The study is on the marine and total environmental distribution and fate of two chemicals, an obsolete pesticide (DDT) and an emerging contaminant (perflu-orinated compound) and contains the first description of a whole historic cycle of an anthropogenic substance, i.e. from the introduction into the environment until its fading beyond phase-out. 

PHYSICAL ORGANIC CHEMISTRY NOMENCLATURE Multicompartment modeling, PHARMACOKINETICS Multicyclic enzyme systems,... 

For multicompartment models, in addition to the retention-time distributions within each compartment, we require the specification of the transition probabilities LJij of transfer among compartments. These ujtJ is, assumed age-invariant, give the probabilities of transfer from a donor compartment i to each possible recipient compartment j. From (9.1), it follows that uiij = hij/ha is the probability that a particle in i will transfer to j on the next departure. 

Consider now a multicompartment structure aiming not only to describe the observed data but also to provide a rough mechanistic description of how the data were generated. This mechanistic system of compartments is envisaged with the drug flowing between the compartments. The stochastic elements describing these flows are the transition probabilities as previously defined. In addition, with each compartment in this mechanistic structure, one can associate a retention-time distribution (a). The so-obtained multicompartment model is referred to as the semi-Markov formulation. The semi-Markov model has two properties, namely that ... 

Another cutoff model, which deals with nonlinearity in biological systems, is one defined by McFarland (191). It attempts to elucidate the dependency of drug transport on hydrophobicity in multicompartment models. McFarland addressed the probability of drug molecules traversing several aqueous lipid barriers from the first aqueous compartment to a distant, final aqueous compartment. The probability of a drug molecule to access the final compartment n of a biological system was used to define the drug concentration in this compartment. 

After an intravenous bolus dose, serum concentrations decrease as if the drug were being injected into a central compartment that not only metabolizes and eliminates drug but also distributes drug to one or more other compartments. Of these multicompartment models, the two-compartment model is encountered most commonly (see Fig. 5-5). After an intravenous bolus injection, serum concentrations decrease in two distinct phases described by the equation ... 

Vancomycin requires multicompartment models to completely describe its serum-concentration-versus-time curves. However, if peak serum concentrations are obtained after the distribution phase is completed (usually V2 to 1 hour after a 1-hour intravenous infusion), a one-compartment model can be used for patient dosage calculations. Also, since vancomycin has a relatively long half-life compared with the infusion time, only a small amount of drug is eliminated during infusion, and it is usually not necessary to use more complex intravenous infusion equations. Thus simple intravenous bolus equations can be used to calculate vancomycin doses for most patients. Although a recent review paper questioned the clinical usefulness of measuring vancomycin concentrations on a routine basis, research articles" " have shown potential benefits in obtaining vancomycin concentrations... 

If the semilog plot of the plasma level against time after an intravenous dose is not a straight line, then the compound may be distributing in accordance with a two-compartment or multicompartment model (figures 3,28 and 3,23). If a two-compartment model is appropriate, then the semilog plot can be resolved... 

The half-life is therefore independent of the initial concentration (CSTART). When multicompartment models have to be used, the half-life is not independent of the start concentration, but is still a useful parameter. Toxins may have extremely different half-lives. Dioxin (2,3,7,8-TCDD) and DDT have half-lives of several years in the human body, whereas the hydroxyl radical probably has a half-life of less than a microsecond. 

Figure 4.9 Mean concentration-time profile for DFMO administered as a 5-min intravenous infusion of 5 and 10 mg/kg. Data are presented in Table 4.4. The shape of the curve indicates that a multicompartment model is needed.

Peak points above terminal line indicate multicompartment model 0 may be needed for data analysis 0... 

As with previous PK models, deriving the multicompartment model equations requires several inherent assumptions. The multicompartment model equations described here require five inherent assumptions about the ADME processes during and after drug delivery. The specific nature and implications of each of these assumptions are described in this section. 

Multicompartment model equations can be written for instantaneous absorption, zero-order absorption, or first-order absorption. For any of these particular absorption situations, the assumptions described previously for the corresponding absorption in one- and two-compartment models remains exactly the same for multicompartment models. 

---