Approach compartmental

Keywords Absorption In silico Mixing tank Maximum absorbable dose Mass balance approach Compartmental absorption Transit models... 

H. J. M. Kramer, J. W. Dijkstra, A. M. Neumann, R. O Meadhra, G. M. van Rosmalen. Modelling of industrial crystalhzers, a compartmental approach using a dynamic flow-sheeting tool. J Cryst Growth 755 1084, 1996. 

Oppenheimer. Like the Chicago-based scientists before him, Oppenheimer and his researchers often clashed with Groves and the project engineers, who preferred to compartmentalize and control information about the project rather than exchange it freely among the scientists. At Los Alamos, Oppenheimer s approach prevailed. 

Other than the different approaches mentioned above, commercial packages such as GastroPlus (Simulations Plus, Lancaster, CA) [19] and IDEA (LionBioscience, Inc. Cambridge, MA) [19] are available to predict oral absorption and other pharmacokinetic properties. They are both based on the advanced compartmental absorption and transit (CAT) model [20], which incorporates the effects of drug moving through the gastrointestinal tract and its absorption into each compartment at the same time (see also Chapter 22). 

Pharmacokinetics is closely related to pharmacodynamics, which is a recent development of great importance to the design of medicines. The former attempts to model and predict the amount of substance that can be expected at the target site at a certain time after administration. The latter studies the relationship between the amount delivered and the observable effect that follows. In some cases the observable effect can be related directly to the amount of drug delivered at the target site [2]. In many cases, however, this relationship is highly complex and requires extensive modeling and calculation. In this text we will mainly focus on the subject of pharmacokinetics which can be approached from two sides. The first approach is the classical one and is based on so-called compartmental models. It requires certain assumptions which will be explained later on. The second one is non-compartmental and avoids the assumptions of compartmental analysis. 

The alternative to compartmental analysis is statistical moment analysis. We have already indicated that the results of this approach strongly depend on the accuracy of the measurement process, especially for the estimation of the higher order moments. In view of the limitations of both methods, compartmental and statistical, it is recommended that both approaches be applied in parallel, whenever possible. Each method may contribute information that is not provided by the other. The result of compartmental analysis may fit closely to the data using a model that is inadequate [12]. Statistical moment theory may provide a model which is closer to reality, although being less accurate. The latter point has been made in paradigmatic form by Thom [13] and is represented in Fig. 39.16. 

The model has its own structure and features, and is a deviation from the TDE, or the compartmental, or stochastic approaches. 

Model selection, application and validation are issues of major concern in mathematical soil and groundwater quality modeling. For the model selection, issues of importance are the features (physics, chemistry) of the model its temporal (steady state, dynamic) and spatial (e.g., compartmental approach resolution) the model input data requirements the mathematical techniques employed (finite difference, analytic) monitoring data availability and cost (professional time, computer time). For the model application, issues of importance are the availability of realistic input data (e.g., field hydraulic conductivity, adsorption coefficient) and the existence of monitoring data to verify model predictions. Some of these issues are briefly discussed below. 

PBPK and classical pharmacokinetic models both have valid applications in lead risk assessment. Both approaches can incorporate capacity-limited or nonlinear kinetic behavior in parameter estimates. An advantage of classical pharmacokinetic models is that, because the kinetic characteristics of the compartments of which they are composed are not constrained, a best possible fit to empirical data can be arrived at by varying the values of the parameters (O Flaherty 1987). However, such models are not readily extrapolated to other species because the parameters do not have precise physiological correlates. Compartmental models developed to date also do not simulate changes in bone metabolism, tissue volumes, blood flow rates, and enzyme activities associated with pregnancy, adverse nutritional states, aging, or osteoporotic diseases. Therefore, extrapolation of classical compartmental model simulations... 

Extending the emulsion to a water-in-oil-in-water mixture allowed further refinement of the IVC concept. Compartmentalization of E. coli containing semm paraoxonase variants allowed the accumulation of fluorescent product to a point where it could be detected by FACS [57]. This approach was also used with in vitro transcription and translation to evolve /3-galactosidase activity from the Ebg gene [58]. 

Another approach, developed in our laboratory, consists of the compartmentalization of the sensing layer25"27. This concept, only applicable for multi-enzyme based sensors, consist in immobilizing the luminescence enzymes and the auxiliary enzymes on different membranes and then in stacking these membranes at the sensing tip of the optical fibre sensor. This configuration results in an enhancement of the sensor response, compared with the case where all the enzymes are co-immobilized on the same membrane. This was due to an hyperconcentration of the common intermediate, i.e. the final product of the auxiliary enzymatic system, which is also the substrate of the luminescence reaction, in the microcompartment existing between the two stacked membranes. 

Refinement and expansion of these steady-state mass balance approaches has led to the development of dynamic models which allow for estimation of the fraction absorbed as a function of time and can therefore be used to predict the rate of dmg absorption [37], These compartmental absorption and transit models (CAT) models have subsequently been used to predict pharmacokinetic profiles of drugs on the basis of in vitro dissolution and permeability characteristics and drug transit times in the intestine [38],... 

The basis for all CAT models is the fundamental understanding of the transit flow of drugs in the gastrointestinal tract. Yu et al. [61] compiled published human intestinal transit flow data from more than 400 subjects, and their work showed the human mean small intestinal transit time to be 199 min. and that seven compartments were optimal in describing the small intestinal transit process using a compartmental approach. In a later work, Yu et al. [58] showed that between 1 and 14 compartments were needed to optimally describe the individual small intestine transit times in six subjects but in agreement with the earlier study, the mean number of compartments was found to be seven. This compartmental transit model was further developed into a compartmental absorption and transit (CAT) model ([60], [63]). The assumptions made for this CAT model was that no absorption occurs in the stomach or in the colon and that dissolution is instantaneous. Yu et al. [59] extended the CAT model... 

The compartmentalization of experimental parameters is not rigorously exact, but provides a useful and practical approach to which further refinements sueh as the distance dependence of the exothermicity [36] and reorganization... 

One approach to compartmentalize hemoglobin is to encapsulate hemoglobin in biodegradable polymer-PEG-polylactide (30). These nanocapsules have a diameter of 80-150 nm and contain superoxide dismutase, catalase, carbonic anhydrase, and other enzymes of Embden-Meyerhof pathway that are needed for long-term function of an oxygen carrier (31,32). The polylactide capsules are metabolized in vivo to water and carbon... 

For the convenience of numerical solution, the continuous reactor is modeled in terms of compartmental analysis, as shown schematically in Figure 4.3. The reactor is modeled as a series of n compartments, each one a homogeneous CSTR [148]. The compartments are all assumed to have the same volume. Applying the compartmental analysis approach enables consideration... 

Applying the compartmental analysis approach leads to equations (32) to (37), which hold for both the basic and the extended basic systems. When the latter is considered, the following equation should also be used ... 

GastroPlus [137] and IDEA [138] are absorption-simulation models based on in vitro input data like solubility, Caco-2 permeability and others. They are based on advanced compartmental absorption and transit (ACAT) models in which physicochemical concepts are incorporated. Both approaches were recently compared and are shown to be suitable to predict the rate and extent of human absorption [139]. 

Although compartmental models and physiologically-based models may at first, seem quite different, and are usually treated as two different classes of models, both approaches are actually similar [17]. When appropriately defined, probably any PB-PK model can be written as a compartmental model and vice versa. This can be seen by comparing the models in Figures 13.1 and 13.3, and their mathematical descriptions in Eq. 13.1 and 13.5. 

---