Kinetics three-compartment model

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.)...

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. 

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). 

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 kinetic study of Stanbury et al. was based on a three compartment model which included intrathyroidal iodine and extrathyroidal pools of organic and inorganic icxline (1). This model was investigated after the administration of a tracer dose of Ij From Ij distribution and freon the sequential modifications of the spedfic aeftivies, it was possible, through this model to deduce the iodine content of these cximpartments and their transfer rate exmstants. (1)... 

The linear model. Equation 9.6, has become very useful in applications due to an important result the kinetics of a tracer in a constant steady-state system, linear or nonlinear, are linear with constant coefficients. An example is shown in Figure 9.3 where the three-compartment model by Cobelli et al. [1984b] for studying tracer glucose kinetics in steady state at the whole-body level is depicted. Linear compartmental models in conjunction with tracer experiments have been extensively used in studying distribution of materials in living systems both at whole-body, organ and cellular level. Examples and references can be found in Carson et al. [1983], Jacquez [1996], and Cobelli et al. [2000], Carson and Cobelli [2001]. 

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. 

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.

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. 

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... 

The earliest models of lead toxicokinetics are typified by that of Rabinowitz et al. (1976, 1977), using stable lead isotope in human volunteers, and which indicate that there are at least three kinetically distinct body compartments for lead disposition in vivo. These compartments consist of a central blood compartment, a second lead depository in peripheral soft tissues, and, finally, the large bone compartment for lead. Lead in blood is the most kinetically labile, whereas lead in soft tissues has a somewhat larger biological half-life. The bone compartment retains lead for the longest time. Blood and soft tissues contain relatively small burdens of lead, ca. 1.9 and 0.6 mg respectively, while the vast majority of the body burden of lead is sequestered in a kinetically slow compartment of bone, with levels that can exceed 200 mg of the toxicant. 

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