The compartment model

The change of concentration in a compartment, e.g., blood or lake water, may be described by a differential equation, 

A fish swimming in a lake with uptake through the gills and elimination through just one biotransformation system, for instance, by an enzyme in the liver, may be regarded as a one-compartment system  

The concentration in the water (Cw) may be constant for some time and a steady-state equilibrium concentration in the fish (CMAX) will be reached. The uptake rate (R), defined as change in fish concentration due to uptake, is proportional to the concentration in the water (R = k x Cw) and is therefore approximately constant. The elimination due to liver metabolism or other first-order processes is proportional to the concentration in the fish. The total change of concentration by time will be the difference of uptake rates and elimination rates. In our simple case, 

By integration and rearranging, remembering that the term k01 x Cw is constant, we get 

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The limited efficacy of classical anticancer diugs can be explained in part by the compartment model of dividing (growth fraction, compartment A) and nondividing (compartment B) cells. The majority of antineoplastic diugs acts upon cycling cells and will hit, therefore, compartment A only. 

Reference Values of Parameters for the Compartment Model to Represent Time-dependent... 

Such high maintenance of cytotoxic activity in the in vitro serum medium and long in vivo circulation of Pt in the blood for DCM-Dex/CDDP conjugate were due to the strength of six-membered chelate-type coordination of the platinum atom with carrier polymer and steric hindrance of carrier polymer. Summarized in Table 2 are the results of the compartment model analysis. The show excretion rate of the Pt complex into urine by the DCM-Dex/CDDP conjugate compared with rapid excretion by the free CDDP in rats supported the longer circulation time for the Pt polymer complex in the blood (Figure 3). 

Flow models can be of different levels of sophistication and the compartment models of this chapter are the next stage beyond the very simplest, those that assume the extremes of plug flow and mixed flow. In the compartment models we consider the vessel and the flow through it as follows ... 

S. Claudel, C. Fonteix, J.P. Leclerc, and H.G. Lintz. Application of the possibility theory to the compartment modelling of flow pattern in industrial processes. Chemical Engineering Science, 58 4005-4016, 2003. 

The choice of the compartment model is mainly driven by the data quality and the frequency of the plasma sampling, e.g. if no samples are taken shortly after the administration of the compound, where most of the distribution processes occur, it might be possible that a simpler model (i.e. one with less compartments) is sufficient to describe the data. 

The compartment model just described can estimate the concentrations of drugs within various ocular tissues. A more complex compartment model that includes drug movement through the posterior aqueous, vitreous, and retina is shown in Figure 2-6. This model becomes useful when a drug is introduced directly into the vitreous or... 

The simplest model is a two-compartment model in which there is a plasma compartment and tissue compartment which have reversible flows of compound or metabolites or both between them. The compartment model for a drug which follows bi-exponential pharmacokinetics is shown below. In addition, the general forms of the equations that describe the rate of change of drug in the two compartments are presented below for both the central (compartment 1, eqn (1)) and the peripheral (compartment 2, eqn (2)) model, respectviely ... 

Table 3-9. Reference Values of Parameters for the Compartment Model to Represent Time-dependent Particle Transport from the Human Respiratory Tract (continued)...

A.2 Application of the Compartment Model to Methyl Chloroform (CH3CCI3)... 

A. 1 Relation Between Atmospheric Mass and Volume Mixing Ratio 114 2.A.2 Application of the Compartment Model to Methyl Chloroform (CH3CCI3) 115... 

This is identical to the result computed for the external unstirred layer problem (cf. Eqns. 62 and 63) and is essentially that computed for the compartment model (Eqns. 

Fig. 8. Volume transport against an adverse osmotic gradient as determined by a comprehensive epithelial simulation. The model includes as variables, the concentrations of Na, K, and Cl, as well as electrical potential intraepithelial concentration gradients are computed and the cell and channel arc represented as compliant structures. Transepithelial volume flow is plotted against mucosal osmolality (serosa fixed at 0.2 mosM) for five values of mucosal water permeability (spanning two orders of magnitude). As predicted by the-compartment model, the strength of transport (intercept with =0) is quite insensitive to mucosal water permeability. (From [15].)...

Because of the complexity of ADME processes, an adequate description of the observations is sometimes possible only by assuming a simplified model the most useful model in pharmacokinetics is the compartment model. The body is conceived to be composed of mathematically interconnected compartments. 

It is important to recognize that the selection of the compartment model is contingent upon the availability of plasma concentration versus time data. Therefore, the model selection process is highly dependent upon the following factors. 

As mentioned above, only the distribution characteristics of a drug play a role in the selection of the compartment model. The chosen model, as well as the route of drug administration, by... 

Fluid flow models, where a simple fluid mechanical model is constructed by dividing the reactor into different zones of macro- and micromixing this is clearly an extension of the compartment models of macromixing but zones of micromixedness are added. 

The noncompartmented model consisted of 73 transformers (reaction rates and transport step), balancing 53 metaboHtes. The compartmented approach was buUt on 95 transformers and 75 metabolites. While most of the simulated fluxes were similar in both approaches, a fraction of approximately 15% of totally available ATP was missing in the compartmented model compared to the noncompartmented approach. This was due to the assumed activity of the citrate-pyruvate shuttle that imports pyruvate (via pyruvate/H+ symporter) into mitochondria by exporting citrate (via citrate/malate antiporter). In cytoplasm, citrate is further... 

Figure 8.2 Simple model. This figure depicts the compartment model, which is comprised of plants Pi), which are the primary producers, herbivores (H/), carnivores (Q), human households (HH), and a resource pool and inaccessible resource pool (RP, IRP).

Figure 8.4 The integrated economic—ecological model. This figure depicts the compartment model, which is comprised of piants (P,), which are the primary producers, herbivores (H/), carnivores (C,), human households (HH), and a resource pool and inaccessible resource pool (RP, IRP). The arrows represent the mass flows from one compartment (origination) to another compartment (termination), and all living compartments have an implied flow back to the resource pool that represents death. IS is the industrial sector, whereas EP and ES are the energy producers and the energy source compartment, respectively [14].

Once baseline has been established and maintained within 3-5% for a satisfactory period, the stimulus is initiated. In accord with the compartment model, an increase in ECF concentration of electroactive species now causes transport into the pool, and the resulting change is seen as an increase of successive ej sec values over time. If linear sweep or DPV measurements are made, only a few recordings may be needed to achieve stable baseline conditions—presumably since the electrolysis depletion occurs over a more extended period of time and the pseudoequilibrium is reached more quickly. 

A second important compartment model comprises eompartments eonsisting of a perfectly mixed segment and a plug-flow segment, which in turn can be represented by a series of perfectly mixed segments (see Fig. 10.14). This compartment model is selected in case segregation is important Equations analogous to those for the compartment model of Fig. 10.13 can be derived. 

Movement of Polymers in the Body Compartments 3.1 The Compartment Model of an Organism... 

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