Noncompartmental modeling

Analysis of most (perhaps 65%) pharmacokinetic data from clinical trials starts and stops with noncompartmental analysis (NCA). NCA usually includes calculating the area under the curve (AUC) of concentration versus time, or under the first-moment curve (AUMC, from a graph of concentration multiplied by time versus time). Calculation of AUC and AUMC facilitates simple calculations for some standard pharmacokinetic parameters and collapses measurements made at several sampling times into a single number representing exposure. The approach makes few assumptions, has few parameters, and allows fairly rigorous statistical description of exposure and how it is affected by dose. An exposure response model may be created. With respect to descriptive dimensions these dose-exposure and exposure-response models... 

Two classical methods used in the analysis of pharmacokinetic data are the fitting of sums of exponential functions (2- and 3-compartment mammillary models) to plasma and/or tissue data, and less frequently, the fitting of arbitrary polynomial functions to the data (noncompartmental analysis). 

A modeT that accounts for the selective degradation of proteins based on the amino acid that is present on the amino- or N-end of nascent proteins. Intracellular processing of nascent, noncompartmentalized proteins generates the mature protein via the action of amino-terminal peptidases. In model studies using /3-galactosidase... 

E.M. Landau and J.J. DiStefano III, Multiexponential, multicompartmental and noncompartmental modeling II, Data analysis and statistical considerations, Am. J. Physiol. 246 (1984) R665-R677. 

Various PK parameters such as CL, Vd, F%, MRT, and T /2 can be determined using noncompartmental methods. These methods are based on the empirical determination of AUC and AUMC described above. Unlike compartmental models (see below), these calculation methods can be applied to any other models provided that the drug follows linear PK. However, a limitation of the noncompartmental method is that it cannot be used for the simulation of different plasma concentration-time profiles when there are alterations in dosing regimen or multiple dosing regimens are used. 

P. Veng-Pedersen. Noncompartmentally based pharmacokinetic modeling. Adv. Drug Deliv. Rev. 48 265-300, 2001. 

In contrast to noncompartmental analysis, in compartmental analysis a decision on the number of compartments must be made. For mAbs, the standard compartment model is illustrated in Fig. 3.11. It comprises two compartments, the central and peripheral compartment, with volumes VI and V2, respectively. Both compartments exchange antibody molecules with specific first-order rate constants. The input into (if IV infusion) and elimination from the central compartment are zero-order and first-order processes, respectively. Hence, this disposition model characterizes linear pharmacokinetics. For each compartment a differential equation describing the change in antibody amount per time can be established. For... 

Traditionally, linear pharmacokinetic analysis has used the n-compartment mammillary model to define drug disposition as a sum of exponentials, with the number of compartments being elucidated by the number of exponential terms. More recently, noncompartmental analysis has eliminated the need for defining the rate constants for these exponential terms (except for the terminal rate constant, Xz, in instances when extrapolation is necessary), allowing the determination of clearance (CL) and volume of distribution at steady-state (Vss) based on geometrically estimated Area Under the Curves (AUCs) and Area Under the Moment Curves (AUMCs). Numerous papers and texts have discussed the values and limitations of each method of analysis, with most concluding the choice of method resides in the richness of the data set. 

A basic assumption related to both methods of analysis is that the elimination of drug from the body is exclusively from the sampling compartment (i. e., blood/ plasma), and that rate constants are first order. However, when some or all of the elimination occurs outside the sampling compartment - that is, in the peripheral or tissue compartment(s) - these types of analysis are prone to error in the estimation of Vss, but not CL. In compartmental modeling, the error is related to the fact that no longer do the exponents accurately reflect the inter-compartmental and elimination (micro) rate constants. This model mis specification will result in an error that is related to the relative magnitudes of the distribution rate constants and the peripheral elimination rate constant. However, less widely understood is the fact that this model mis specification will also result in errors in noncompartmental pharmacokinetic analysis. 

PKPlus module to rapidly fit PK parameters to IV plasma concentration-time (Cp-time) data for noncompartmental and 1-, 2-, 3-compartment models. 

Conversely, some substances are transported relatively slowly to their site of degradation, transformation, or excretion, so that the rate of diffusion limits their rate of removal from the system. Substances of this nature are best described by noncompartmental models and power functions. 

Noncompartmental models were introduced as models that allow for transport of material through regions of the body that are not necessarily well mixed or of uniform concentration [248]. For substances that are transported relatively slowly to their site of degradation, transformation, or excretion, so that the rate of diffusion limits their rate of removal from the system, the noncompartmental model may involve diffusion or other random walk processes, leading to the solution in terms of the partial differential equation of diffusion or in terms of probability distributions. A number of noncompartmental models deal with plasma time-concentration curves that are best described by power functions of time. 

As mentioned above, many drugs do not conform to the simple one-compartment model. These cases may require a two- or three-compartment model characterized by a hi- or tri-exponential decline (8). Alternatively, a simpler, commonly used approach is noncompartmental analysis, in which the concentration time profile is treated descriptively by the method of... 

From previous chapters it is clear that the evaluation. of pharmacokinetic parameters is an essential part of understanding how drugs function in the body. To estimate these parameters studies are undertaken in which transient data are collected. These studies can be conducted in animals at the preclinical level, through all stages of clinical trials, and can be data rich or sparse. No matter what the situation, there must be some common means by which to communicate the results of the experiments. Pharmacokinetic parameters serve this purpose. Thus, in the field of pharmacokinetics, the definitions and formulas for the parameters must be agreed upon, and the methods used to calculate them understood. This understanding includes assumptions and domains of validity, for the utility of the parameter values depends upon them. This chapter focuses on the assumptions and domains of validity for the two commonly used methods — noncompartmental and compartmental analysis. Compartmental models have been presented in earlier chapters. This chapter expands upon this, and presents a comparison of the two methods. 

How does one resolve the difficulty associated with partial differential equations The most common way is to reduce the system into a finite number of components. This can be accomplished by lumping together processes based upon time or location, or a combination of the two. One thus moves from partial derivatives to ordinary derivatives, where space is not taken directly into account. This reduction in complexity results in the compartmental models discussed later in this chapter. The same lumping process also forms the basis for the noncompartmental models discussed in the next section, although the reduction is much simpler than for compartmental models. 

The pharmacokinetic parameters descriptive of the system are as follows (although these definitions apply to both noncompartmental and compartmental models, some modification will be needed for two accessible pool models as well as compartmental models) ... 

The noncompartmental model provides a framework to introduce and use statistical moment analysis... 

The kinetic parameters of the noncompartmental model are those defined previously for the accessible pool and system. However/ the formulas depend upon the experimental protocol/ especially on the mode of drug administration. In this chapter/ only the canonical inputs will be considered/ such as an intravenous bolus (or multiple boluses) or constant infusion (or multiple constant infusions). References will be given for those interested in more complex protocols. 

The relationships among the accessible pool parameters in the noncompartmental model are given in the following equations ... 

The relationships among the system parameters for the noncompartmental model are... 

There are several reasons for going first to this level of generality for the n-compartment model. First/ it points out clearly that the theories of noncompartmental and compartmental models are very different. While the theory underlying noncompartmental models relies more on statistical theory/ especially in developing residence time concepts [see/ e.g./ Weiss (11)]/ the theory underlying compartmental models is really the theory of ordinary/ first-order differential equations in which/ because of the nature of the compartmental model applied to biological applications/ there are special features in the theory. These are reviewed in detail in Jacquez and Simon (5)/ who also refer to the many texts and research articles on the subject. 

If one has pharmacokinetic data and knows that the situation calls for nonlinear kinetics, then compartmental models, no matter how difficult to postulate, are really required. Noncompartmental models cannot deal with the time-varying situation. 

However, more can be said about the i5 y that is important in comparing compartmental and noncompartmental models. Suppose there is a generic input into compartment 1 only, f iq (remember, in this... 

In comparing noncompartmental with compartmental models, it should now be clear that this is not a question of declaring one method better than the other. It is a question of (1) what information is desired from the data and (2) what is the most appropriate method to obtain this information. It is hoped that the reader of this chapter will be enabled to make an informed decision on this issue. 

This discussion will rely heavily on the following sources. First, the publications of DiStefano and Landaw (22, 23) deal with issues related to compartmental versus single accessible pool noncompartmental models. Second, Cobelli and Toffolo (3) discuss the two accessible pool noncompartmental model. Finally, Coveil et al. (4) provide the theory to demonstrate the link between noncompartmental and compartmental models in estimating the pharmacokinetic parameters. 

Suppose one has a set of pharmacokinetic data. The question is how to obtain information from the data related to the disposition of the drug in question. DiStefano and Landaw (22) deal with this question by making the distinction between models of data and models of system. Understanding this distinction is useful in understanding the differences between compartmental and noncompartmental models. 

As discussed, the noncompartmental model divides the system into two components an accessible pool and nonaccessible pools. The kinetics of the nonacces-sible pools are lumped into the recirculation-exchange arrows. From this, as has been discussed, we can estimate pharmacokinetic parameters describing the accessible pool and system. 

When are the parameter estimates from the noncompartmental model equal to those from a linear, constant-coefficient compartmental model As DiStefano and Landaw (22) explain, they are equal when the equivalent sink and source constraints are valid. The equivalent source constraint means that all... 

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