Three-compartment kinetics

The first step in performing PK modeling is to graph the plasma concentration versus time profile to examine the shape of the curve and to get some preliminary ideas whether the data would fit a one-, two- or a three-compartment PK model. From the semi-logarithmic plot (Figure 1), it was obvious that the compound exhibited either two- or three-compartment kinetics. 

It manifests a three-compartment kinetics, having the half-lives of 0.08, 2.3 and 8.5 hour respectively.lt is usualty secreted direetly into the bile upto 70%. Nearly 12% gets exereted in urine. As the drug cannot penetrate into the brain therefore, it has a little usage for the CNS leukemias. 

An ideal pharmacokinetic model of the percutaneous absorption process should be capable of describing not only the time course of penetration through skin and Into blood (or receptor fluid In a diffusion cell), but also the time course of disappearance from the skin surface and accumulation (reservoir effect) of penetrant within the skin membrane. Neither Pick s Plrst Law of Diffusion nor a simple kinetic model considering skin as a rate limiting membrane only Is satisfactory, since neither can account for an accumulation of penetrant within skin. To resolve this dilemma, we have analyzed the In vitro time course of absorption of radiolabeled benzoic acid (a rapid penetrant) and paraquat (a poor penetrant) through hairless mouse skin using a linear three compartment kinetic model (Figure 5). The three compartments correspond to the skin surface (where the Initial dose Is deposited), the skin Itself (considered as a separate compartment), and the receptor fluid In the diffusion cell. The Initial amount deposited on the skin surface Is symbolized by XIO, and K12 and K23 are first order rate constants. 

Benzodiazepines may depict two- or three-compartment disposition kinetics. For example, a benzodiazepine derivative given in a suitable dose at night may impose dose-dependent effects, in that the concentration attained at night may be in the hypnotic range, whereas the concentration of the drug or its active metabolite or metabolites during the following day may be sufficient to produce antianxiety effects. 

Figure 1.4 Glucose kinetics three-compartment model. Gex, exogenous glucose Gend, glucose produced by gluconeogenesis Gk, glucose eliminated via the kidney BG, blood glucose IG, subcutaneous interstitial glucose. (See the color version of this figure in Color Plates section.)...

Figure 19 Three-compartment cell for studies of the kinetics of the hydrogen evolution reaction on Pt. The lines between the chambers prevent mixing but allow ionic conduction.

Figure 22 Three-compartment cell for studies of the kinetics of iron dissolution in acid.

The experimental data and the calculated curve are plotted in Figure 1. The type of Equation 1 implies a three-compartment system with first-order absorption, that is, at least three kinetically distinguishable pools for ascorbic acid are reflected in the plasma. From the data available it... 

The decay pattern of plasma radioactivity (Figure 1) indicated that a three-compartment model could be chosen for calculation of the kinetic data. The chosen model consists of a central compartment (Figure 2) into which dietary ascorbate is absorbed and from which it is eliminated unchanged. Two other compartments are equilibrated with the central compartment. In compartment 2 the metabolism is assumed to take place and from this compartment metabolites are eliminated. Compartment 3 is a deep pool that acts as a storage compartment. 

What the analysis of distribution makes evident is that the body is a heterogenous collection of compartments. This is reflected in the fact that the elimination of a drug, as described in Figure 9.15 as a simple first order process, often does not, in fact, follow such simple kinetics. The first order process shown in Figure 9.15 assumes that the drug enters and leaves a single compartment. However, if the drug enters and leaves a more complex system (such as a system of two or three compartments in series or... 

Three special cases are considered for the one-compartment zero-order absorption model. First is the extension of the IV infusion equations to cover steady extravascular drug delivery. Second is the use of the one-compartment zero-order absorption model to approximate the plasma concentrations of drugs that follow two-compartment kinetics. The last case... 

The elimination kinetics of bismuth have been described as a three-compartment model with half-lives of 3.5 minutes, 0.25 hour, and 3.2 hours (Slikkerveer and de Wolff 1989). Biological half-times in human have also been reported whole body retention 5 days, kidney 6 days, liver 15 days, spleen 10 days, and bone 13.3 days (IRCP 1960, Fowler and Wouk 1986). 

Kinetic studies in man show that the lead body burden consists essentially of three compartments (1) a rapid exchange pool in blood and soft tissues (2) an intermediate exchange pool in muscles, skin and bone marrow (3) a slow exchange pool in dense bones and teeth (biological half-life about 20 years). The amount of lead stored in the latter compartment increases throughout life (Steenhout, 1982 Steenhout and Pourtois, 1981). 

Fig. 2. Specifying the reactions, (a) Molecular species are divided into three adjacent regions, EC (extracellular), CM (cell membrane), and /C (intracellular). Reactions can be specified in any of these three compartments, (b) In the Reaction Kinetic Editor, we specify the reaction rate expression, as well as the kinetic reaction rates associated with the expression. (c) In this model, the reactions are defined in CM. Solid lines going from molecular species to reaction sites connect reactants solid lines going from reaction sites to molecular species connect products and dotted lines connect enzymes to reaction sites.

The daily elimination in untreated people is estimated at 12 ixg [12] including 2.9 xg excreted with the urine [27]. Ingested bismuth from therapeutics is mainly eliminated with feces as sulfide. Within 5 days 10-20% is excreted. But elimination is not finished after 10 days. Overall 99% may be eliminated in this way [3,12,17,29]. Absorbed bismuth is mainly excreted by urine the biliary/fecal elimination route is only about half of the urinary one [3,6,62-64]. Half-lives in blood after a single dose or during a treatment depend on the kind of the Bi compound, the amounts ingested, and the blood levels. Elimination from blood of bismuth subcitrate is biphasic [17,28,65]. In cases of encephalopathy with remarkably high urine and blood levels (2000 and 1500 p-g/liter, respectively), half-lives were calculated for urine (4.5 days) and blood (5.2 days). Liquor levels decreased more slowly with a half-life of 15.9 days [53]. Elimination kinetics is also described as a three-compartment model with half-lives of 3.5 min, 0.25 hr, and 3.2 hr [6]. Biological half-times in humans are reported for the whole body 5 days, the kidney 6 days, and the liver 15 days (cited in [3]). 

The Rabinowitz et al. model was perhaps the first widely recognized mechanistic model in the sense that it was constructed of kinetic components. It consists of a classical compartmental construction representing internal Pb movement under steady-state or near-steady-state conditions. Its principal features are set forth in Figure 9.2. Mathematically, the model employs coupled differential equations with linear exponential solutions and assumes connected, well-mixed pools for Pb deposition and interorgan movement. Three compartments, one of which is taken to be the central or blood compartment, were resolved via data gathered from ingestion of a stable Pb... 

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