Analysis compartmental

The equation above states that the net content in any compartment i equals the sum of all inflows from the other compartments minus the sum of all outflows towards the other compartments. Such a relation is also referred to as a mass balance differential equation, which is well-known in chemical engineering. In the 

An additional problem arises when the exchange processes are rate-limited. This may be caused by enzymes that become saturated when all their active sites are occupied by the drug, or it may be due to adsorbing proteins that have a limited binding capacity. In such cases, one obtains a type of Michaelis-Menten kinetics of the form  

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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 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... 

As we have shown above, pharmacokinetic compartmental analysis requires estimates of the transfer constants and the volume of distribution Vp from... 

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 phytofiltration of Pb(II) and Cd(II) has been also studied using species of Salvinia. S. minima Baker is a small free-floating aquatic fern native to Mexico, Central America and South America. It has been proved to be an excellent aquatic phytoremediator and hyperaccumulator of Cd(II) and Pb(II).72,76 The relevance of using a compartmentalization analysis (CA) complementary to the use of BCFs and metal removal kinetics by plants has been demonstrated using S. minima... 

JJ DiStefano III. Noncompartmental vs. compartmental analysis Some bases for choice. Am J Physiol 243 R1-R6, 1982. 

Global compartmental analysis can be used to recover association and dissociation rate constants in some specific cases when the lifetimes are much shorter than the lifetimes for the association and dissociation processes. An example is the study for the binding dynamics of 2-naphthol (34, Scheme 14) with / -CD.207 Such an analysis is possible only if the observed lifetimes change with CD concentration and at least one of the decay parameters is known independently, in this case the lifetime of the singlet excited state of 33 (5.3 ns). From the analysis the association and dissociation rate constants, as well as intrinsic decay rate constants and iodide quenching rate constants, were recovered. The association and dissociation rate constants were found to be 2.5 x 109M-1 s 1 and 520 s 1, respectively.207... 

The environmental impact of a new product needs to be assessed before it can be released for general use. Chemicals released into the environment can enter the food chain and be concentrated in plants and animals. Aquatic ecosystems are particularly sensitive, in this respect, since chemicals, when applied to agricultural land, can be transported in the ground water to rivers and then to the lakes, where they can accumulate in fish and plant life. The ecokinetic model presented here is based on a simple compartmental analysis and is based on laboratory ecosystem studies (Blau et ah, 1975). The model is useful in simulating the results of events, such as the accidental spillage of an agrochemical into a pond, where it is not ethical to perform actual experimental studies. 

Consideration of these data in terms of multi-compartmental analysis is found in Fig. 5. The renal compartment never achieved more than 6.3% of the administered dose and declined rapidly after 1 hr. As early as 10 min. the hepatic compartment contained about 18% of the administered compound where a peak value occurred at 2 hrs. and continued to contain large amounts of phenol red for up to 12 hrs. There is only a slight difference between the amount of phenol red handled by the urinary and biliary compartments in 48 hrs., 40% and 48% respectively. In each compartment most of the material is free drug. 

Chawla MK, Lin G, Olson K, Vazdarjanova A, Burke SN, et al. 2004. 3D-catFISH a system for automated quantitative three-dimensional compartmental analysis of temporal gene transcription activity imaged by fluorescence in situ hybridization. J Neurosci Meth 139 13-24. 

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... 

In Section 4.1.4.1 results of numerical simulations were presented for the case when the basic system is operated as a fed-batch reactor. In this section, results of the numerical simulations are presented for the case when the basic system is operated in continuous reactors. The results were obtained for several reactor types. In terms of compartmental analysis (see Section 4.1.3.2) these types are determined by the number of compartments (n) considered to make up the reactor (see Figure 4.3). Three cases are presented here n = ... 

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 ... 

Enzyme-based biochemical networks can be designed and analyzed using basic principles of enzyme kinetics and compartmental analysis procedures. 

Here Cbrain is the brain concentration after correction for intravascular content, and AUC is determined between time 0 and the final sampling time. Two assumptions must hold when interpreting the evaluation in the simple form described above (1) the brain uptake of the compound is linear, meaning is dose independent, and (2) the analysis is performed within a time-frame where the efflux from tissue is negligible (tissue concentrations are sufficiently low compared to plasma concentrations). Violation of these assumptions requires adjustments in experimental design and evaluation. For example, nonlinear kinetics may be accounted for by incorporation of a MichaeUs-Menten term, while efflux can be treated by compartmental analysis [46]. 

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... 

The total amount or mass of a tracee in a pool, corresponding to the volume of distribution (V) multiplied by the tracee concentration in the same pool frequently abbreviated Qx- See Compartmental Analysis... 

A term used in compartmental analysis to designate the appearance of a tracee in its pool (or, more properly, its volume of distribution), the result from tracee biosynthesis and/or tracee transit from another pool. See... 

The labeled form of a metabolite, drug, or other substance used in a kinetic analysis of tracee biosynthesis/ entry (appearance) and tracee catabolism/clearance (disappearance). See Compartmental Analysis... 

A parameter used as a measure of isotope enrichment in stable isotope exchange and compartmental analysis experiments ... 

ASPARTATE CARBAMOYLTRANSFERASE ATMOSPHERE ATOM PERCENT EXCESS TRACER/TRACEE RATIO COMPARTMENTAL ANALYSIS ISOTOPE EXCHANGE KINETICS ATOMIC MASS UNIT ATOMIC ORBITAL ATOMIZATION ATP... 

COMMITMENT-TO-CATALYSIS RAPID EQUILIBRIUM ASSUMPTION KINETIC ISOTOPE EFFECT ISOTOPE TRAPPING COMPARTMENTAL ANALYSIS CATENARY MODEL... 

ATOM PERCENT EXCESS OXYGEN ISOTOPE EXCHANGE COMPARTMENTAL ANALYSIS ISOTOPE EXCHANGE KINETICS GRAPHICAL METHODS... 

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