Multicompartment distribution

Despite their theoreticaUy poor washing performance, due to uneven wash distribution and excessive mn-off because the filter surface is not horizontal, many multicompartment dmm filters continue to be used as cake washing filters. Effective washing of the filter cloth can be done only with the belt discharge type, where the cloth leaves the dmm for a brief period and can thus be washed on both sides. 

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. 

Figure 5. Time course of distribution of phenol red in terms of multicompartment analysis (8)...

The multicompartment equipment of Figure 12.17(c) permits improved control of process conditions and may assure a narrower size distribution because of the approach to plug flow. 

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 ... 

The three estimates of distribution volume that we have encountered have slightly different properties (24). Of the three, Vd(ss) has the strongest physiologic rationale for multicompartment systems of drug distribution. It is independent of the rate of both drug distribution and elimination, and is the volume that is referred to in Equations 3.1 and 3.2. On the other hand, estimates of V ( area) most useful in clinical pharmacokinetics, since it is this volume that links elimination clearance to elimination half-life in the equation... 

FIGURE 4.5 Multicompartment system used to model the kinetics of NAPA absorption, distribution, and elimination. NAPA labeled with was injected intravenously (IV) to define the kinetics of NAPA disposition. NAPA distribution from intravascular space (Vq) to fast (Vp) and slow (Vg) equilibrating peripheral compartments is characterized by the intercompartmental clearances CLp and CLg. NAPA is cleared from the body by both renal (CLj ) and nonrenal (CLjyj ) mechanisms. A NAPA tablet was administered orally with the intravenous dose to analyze the kinetics of NAPA absorption from the gastrointestinal (GI) tract. After an initial delay that consisted of a time lag (not shown) and presumed delivery of NAPA to the small bowel (feg), the rate and extent of NAPA absorption were determined by ka and ko, as described in the text. (Reproduced with permission from Atkinson AJ, Jr. et al. Clin Pharmacol Ther 1989 46 182-9.)... 

Vancomycin is approximately 30 to 55% bound to plasma proteins. Its distribution after intravenous administration proceeds as a biphasic process and is consistent with a two or three compartment model. The half-life of the first distributive phase is approximately 0.4 hour in patients with normal renal function the second distributive phase is approximately 1.6 hours [172]. Consistent with its multicompartment pharmacokinetic modeling, vancomycin is widely distributed and penetrates into many different body fluids and... 

Dose-response models describe a cause-effect relationship. There are a wide range of mathematical models that have been used for this purpose. The complexity of a dose-response model can range from a simple one-parameter equation to complex multicompartment pharmacokinetic/pharmacodynamic models. Many dose-response models, including most cancer risk assessment models, are population models that predict the frequency of a disease in a population. Such dose-response models typically employ one or more frequency distributions as part of the equation. Dose-response may also operate at an individual level and predict the severity of a health outcome as a function of dose. Particularly complex dose-response models may model both severity of outcome and population variability, and perhaps even recognize the influence of multiple causal factors. 

For a one-compartment elimination, the visualization and quantification of elimination is straightforward. However, for a multicompartment system consisting of distribution followed by elimination, two (or more) half lives can be calculated. Usually, the first and most rapid t1/2 relates to drug distribution, while the second (slower) t relates to elimination (and therefore is of more clinical relevance see Figure 9.20). However, as was seen in Figure 9.17A, if the distribution relates to a therapeutically relevant compartment, such as the brain for diazepam treatment of epilepsy, then the first t1/2 may also be therapeutically relevant. 

W. Krzyzanski and W. J. Jusko, Indirect pharmacodynamic models for response with multicompartment distribution or polyexponential disposition. J Pharmacokinet Bio-pharm 28 57-78 (2002). 

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... 

In a drug discovery environment, the elimination rate is used to estimate accumulation after multiple dosing. Many terms of half-lives were introduced with the attempt to simplify multicompartment kinetics for the estimation of accumulation. A recent article by Sahin and Benet compared and commented on various terms of half-life [32], The accumulation after multiple dosing is not only a function of elimination rate but also a function of dosing interval for multicompartmental distribution compounds. In addition, the accumulation of Cmax is a function of absorption rate [32], Furthermore, the accumulation for Cmax, Cmin, and AUC can be different with the same compound and same dosing interval. Therefore, the half-life calculated based on accumulation ratios from different exposure parameters and with different dosing intervals for the same compound can be different. It is not practical to use... 

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... 

Each of the exponential decay terms in the generalized multicompartment models represent a distinct phase or change in shape of the plasma concentration versus time curve. The extra (n+l) exponential term for first-order absorption always has the absorption rate constant (ka) in the exponent, and always represents an absorption phase. The exponential term with the smallest rate constant (A ) always represents the elimination phase, and this rate constant always represents the elimination rate constant and always equals the terminal line slope m= — A J. All other exponential terms represent distinct distribution phases caused by the different rates of distribution to different tissue compartments. 

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