Model modeling compartmental

One of several general models for metabolite compart-mentation in which a central compartment is directly linked to or feeds from (hence the name) other compartments that do not communicate with each other aside from their connection to the central pool. See Catenary Model Compartmental Analysis... 

MALTOSE 1-EPIMERASE MALTOSE PHOSPHORYLASE MALTOSE PHOSPHORYLA.se MALYL-CoA LYASE MAMILLARY MODEL CATENARY MODEL COMPARTMENTAL ANALYSIS Mandelate,... 

Ozkaynak, H., P. B. Ryan, G. A. Allen, and W. A. Turner, Indoor Air Quality Modeling Compartmental Approach with Reactive Chemistry, Environ. Int., 8, 461-471 (1982). 

The purpose of this article is to introduce the reader to simple basic concepts and principles of pharmacokinetic/toxicokinetic analysis using both types of models - compartmental and physiologically based. 

Figure 3. Model compartmentalization, upper boundary and tributary...

In what follows, both macromixing and micromixing models will be introduced and a compartmental mixing model, the segregated feed model (SFM), will be discussed in detail. It will be used in Chapter 8 to model the influence of the hydrodynamics on a meso- and microscale on continuous and semibatch precipitation where using CFD, diffusive and convective mixing parameters in the reactor are determined. 

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

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. 

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). 

The measurement of carotenoid absorption is fraught with difficulties and riddled with assumptions, and it is therefore a complex matter. Methods may rely on plasma concentration changes provoked by acute or chronic doses, oral-faecal mass balance method variants and compartmental modelling. 

Fig. 10. Mechanisms of steady-slqte kinetics of sugar phosphorylation catalyzed by E-IIs in a non-compartmentalized system. (A) The R. sphaeroides 11 model. The model is based on the kinetic data discussed in the text. Only one kinetic route leads to phosphorylation of fructose. (B) The E. coli ll " model. The model in Fig. 8 was translated into a kinetic scheme that would describe mannitol phosphorylation catalyzed by Il solubilized in detergent. Two kinetic routes lead to phosphorylation of mannitol. Mannitol can bind either to state EPcy, or EPpe,. E represents the complex of SF (soluble factor) and 11 and II in A and B, respectively. EP represents the phosphorylated states of the E-IIs. Subscripts cyt and per denote the orientation of the sugar binding site to the cytoplasm and periplasm, respectively. PEP, phosphoenolpyruvate.

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 synthetic data have been obtained by adding random noise with standard deviation of about 0.4 )0.g 1 to the theoretical plasma concentrations. As can be seen, the agreement between the estimated and the computed values is fair. Estimates tend to deteriorate rapidly, however, with increasing experimental error. This phenomenon is intrinsic to compartmental models, the solution of which always involves exponential functions. 

Usually, the buffer compartment is not accessible and, consequently, the absolute amount of X cannot be determined experimentally. For this reason, we will only focus our discussion on the plasma concentration Cp. It is important to know, however, that the time course of the contents in the two compartments is the sum of two exponentials, which have the same positive hybrid transfer constants a and p. The coefficients A and B, however, depend on the particular compartment. This statement can be generalized to mammillary systems with a large number of compartments that exchange with a central compartment. The solutions for each of n compartments in a mammillary model are sums of n exponential functions, having the same n positive hybrid transfer constants, but with n different coefficients for each particular compartment. (We will return to this property of linear compartmental systems during the discussion of multi-compartment models in Section 39.1.7.)... 

We now turn our attention to the graphical determination of the various parameters of our two-compartmental model, i.e. the plasma volume of distribution Vp,... 

Fig. 39.14. (a) Catenary compartmental model representing a reservoir (r), absorption (a) and plasma (p) compartments and the elimination (e) pool. The contents X, Xa, Xp and X,. are functions of time t. (b) The same catenary model is represented in the form of a flow diagram using the Laplace transforms Xr, Xa and Xp in the j-domain. The nodes of the flow diagram represent the compartments, the boxes contain the transfer functions between compartments [1 ]. (c) Flow diagram of the lumped system consisting of the reservoir (r), and the absorption (a) and plasma (p) compartments. The lumped transfer function is the product of all the transfer functions in the individual links. 

The quantities AUMC and AUSC can be regarded as the first and second statistical moments of the plasma concentration curve. These two moments have an equivalent in descriptive statistics, where they define the mean and variance, respectively, in the case of a stochastic distribution of frequencies (Section 3.2). From the above considerations it appears that the statistical moment method strongly depends on numerical integration of the plasma concentration curve Cp(r) and its product with t and (r-MRT). Multiplication by t and (r-MRT) tends to amplify the errors in the plasma concentration Cp(r) at larger values of t. As a consequence, the estimation of the statistical moments critically depends on the precision of the measurement process that is used in the determination of the plasma concentration values. This contrasts with compartmental analysis, where the parameters of the model are estimated by means of least squares regression. 

Compartmental analysis is the most widely used method of analysis for systems that can be modeled by means of linear differential equations with constant coefficients. The assumption of linearity can be tested in pharmaeokinetic studies, for example by comparing the plasma concentration curves obtained at different dose levels. If the curves are found to be reasonably parallel, then the assumption of linearity holds over the dose range that has been studied. The advantage of linear... 

Fig. 39.16. Paradigm for the fitting of sums of exponentials from a compartmental model (c) to observed concentration data (o) as contrasted by the results of statistical moment analysis (s). (After Thom [13].)...

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. 

Modeled rates (curve d. Fig. 5) agreed with those determined experimentally. We suggest that the interaction of mass transfer and metabolism consisting of two or several bioreactions in compartmentalized media is an interesting phenomenon, which has not been fully researched to date. 

The ICRP (1994b, 1995) developed a Human Respiratory Tract Model for Radiological Protection, which contains respiratory tract deposition and clearance compartmental models for inhalation exposure that may be applied to particulate aerosols of americium compounds. The ICRP (1986, 1989) has a biokinetic model for human oral exposure that applies to americium. The National Council on Radiation Protection and Measurement (NCRP) has also developed a respiratory tract model for inhaled radionuclides (NCRP 1997). At this time, the NCRP recommends the use of the ICRP model for calculating exposures for radiation workers and the general public. Readers interested in this topic are referred to NCRP Report No. 125 Deposition, Retention and Dosimetry of Inhaled Radioactive Substances (NCRP 1997). In the appendix to the report, NCRP provides the animal testing clearance data and equations fitting the data that supported the development of the human mode for americium. 

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