Non-compartmental model

Heterogeneous drugs with A 0 their kinetics are described with non-compartmental modeling, and in reality they approximate the true heterogeneous disposition, i.e., the time-dependent character of diffusion (flow). These drugs are characterized by high volumes of distribution. 

The pharmacokinetic values in the blood and milk given in Table 4 were calculated by the pharmacokinetics software WinNonlin, Version 1.1. using the mean concentrations, a non-compartmental model and the linear trapezoidal rule. 

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. 

Non-compartmental or model-independent approaches to pharmacokinetics Pharmacodynamics of drug action Pharmacokinetic-pharmacodynamic models INTRODUCTION... 

This definition remains model-dependent, but VDSS can be calculated using a non-compartmental approach, which does not require any assumptions about the pharmacokinetic model concerned (see below). 

A liquid chromatography/tandem mass spectrometry (LC/MS/MS) method was developed [33] and validated for the determination of donepezil in human plasma samples. Diphenhydramine was used as the IS. The collision-induced transition m/z 380 > 91 was used to analyze donepezil in selected reaction monitoring mode. The signal intensity of the m/z 380 —> 91 transition was found to relate linearly with donepezil concentrations in plasma from 0.1 to 20.0 ng/ml. The lower limit of quantification of the LC/MS/MS method was 0.1 ng/ml. The intra- and inter-day precisions were below 10.2% and the accuracy was between 2.3% and +2.8%. The validated LC/MS/MS method was applied to a pharmacokinetic study in which healthy Chinese volunteers each received a single oral dose of 5 mg donepezil hydrochloride. The non-compartmental pharmacokinetic model was used to fit the donepezil plasma concentration-time curve. Maximum plasma concentration was... 

Half-lives were calculated by the pharmacokinetics software WinNonlin, version 1.5. In case of the intravenous administration, a 2 compartmental model was chosen in case of oral administration, a non-compartmenal model. The AUCs were calculated using the linear trapezoidal rule. The results are summarized in Table 3. 

The model independent pharmacokinetic characteristics for XYZ1234 following single dose administration of the different treatments were calculated using non-compartmental procedures. The following table gives the arithmetic means, standard deviations, and coefficients of variation as well as the medians and ranges of the primary pharmacokinetic measure AUCo-co, and of the secondary measures Cm, Cmax and MRT. 

Pentikis, H.S. Henderson, J.D. Tran, N.L. Ludden, T.M. Bioequivalence individual and population compartmental modeling compared to the non-compartmental approach. Pharm. Res. 1996, 75, 1116-1121. 

When the dose of a drug is administered as an intravenous bolus, the volume of distribution at steady-state (Vd(ss)) can be calculated. This parameter represents the volume in which a drug would appear to be distributed during steady-state if the drug existed throughout that volume at the same concentration as in the measured fluid (plasma or blood). The volume of distribution at steady-state is generally calculated by a non-compartmental method, which is based on the use of areas (Benet Galeazzi, 1979) and does not require the application of a compartmental pharmacokinetic model or mathematical description of the disposition curve ... 

The advantages of using non-compartmental methods for calculating pharmacokinetic parameters, such as systemic clearance (CZg), volume of distribution (Vd(area))/ systemic availability (F) and mean residence time (MRT), are that they can be applied to any route of administration and do not entail the selection of a compartmental pharmacokinetic model. The important assumption made, however, is that the absorption and disposition processes for the drug being studied obey first-order (linear) pharmacokinetic behaviour. The first-order elimination rate constant (and half-life) of the drug can be calculated by regression analysis of the terminal four to six measured plasma... 

The principal parameter used to indicate the rate of drug absorption is Cmax, even though it is also influenced by the extent of absorption the observed fmaX is less reliable. Because of the uncertainty associated with Cmax, it has been suggested (Endrenyi Yan, 1993 Tozer, 1994) that Cmax/AUCo-loq/ where AUCo-loq is the area under the curve from time zero to the LOQ of the acceptable analytical method, may more reliably measure the rate of drug absorption, except when multiexponential decline is extensive. Estimation of the terms should be based on the observed (measured) plasma concentrationtime data and the use of non-compartmental methods rather than compart-mental pharmacokinetic models. MRTs, from time zero to the LOQ of the analytical method, for the test and reference products can be compared, assuming that first-order absorption and disposition of the drug apply (Jackson Chen, 1987). 

Several models have been suggested to simulate the behavior inside a reactor [53, 71, 72]. Accordingly, homogeneous flow models, which are the subject of this chapter, may be classified into (1) velocity profile model, for a reactor whose velocity profile is rather simple and describable by some mathematical expression, (2) dispersion model, which draws analogy between mixing and diffusion processes, and (3) compartmental model, which consists of a series of perfectly-mixed reactors, plug-flow reactors, dead water elements as well as recycle streams, by pass and cross flow etc., in order to describe a non-ideal flow reactor. 

We began modeling under the assumption that the introduction of the tracer (mass) into the system did not affect the mechanisms present for metabolism of the tracee. The compartmental model was compatible with the assumption that non-steady-state mechanisms for metabolism of /3-carotene were not induced by the tracer because the model prediction of the tracer state, the tracee state, and the steady state could be achieved using the same set of fractional transfer coefficients (FTCs). The appropriateness of this assumption is discussed again under Statistical Considerations. FTC is the fraction of analyte in a donor compartment that is transferred to a recipient compartment per unit of time, in this case per day. 

In recent years, non-compartmental or model-independent approaches to pharmacokinetic data analysis have been increasingly utilized since this approach permits the analysis of data without the use of a specific compartment model. Consequently, sophisticated, and often complex, computational methods are not required. The statistical or non-compartmental concept was first reported by Yamaoka in a general manner and by Cutler with specific application to mean absorption time. Riegelman and Collier reviewed and clarified these concepts and applied statistical moment theory to the evaluation of in vivo absorption time. This concept has many additional significant applications in pharmacokinetic calculations. 

In many cases pharmacokinetic data (i.e. plasma drug concentration versus time data) cannot be fitted to an explicit equation equivalent to a system containing a discrete number of compartments into which dmg distributes. This data analysis requires some form of non-compartmental analysis (also referred to as model-independent analysis.) This is achieved by the use of statistical moment theory. 

For a dmg administered orally, MRT is the sum of time spent in the gastrointestinal tract (mean absorption time) as well as time spent in the rest of the body. In the case of a one-compartment model drug, the mean absorption time is actually equal to the reciprocal of the absorption rate constant (Eq. A.55) and is, therefore, proportional to the absorption half life. For non-compartmental analysis, the mean absorption time is still a good indicator of the rate of drug absorption. In order to get an estimate of mean absorption time in the non-compartmental situation, the drug is administered both orally and intravenously to a subject. Then ... 

Compartmental modeling involves the specification of a structural mathematical model (commonly using either explicit or ordinary differential equations) and system parameters are estimated from fitting the model to pharmacokinetic data via non linear regression analysis or population mixed effects modeling. One popular structural model is the open two-compartment model shown in Figure 6.10. 

A special case in dissolution-limited bioavailability occurs when the assumption of sink condition in vivo fails that is, the drug concentration in the intestine is dose to the saturation solubility. Class IV compounds, according to BCS, are most prone to this situation due to the combination of low solubility and low permeability, although the same could also happen for class II compounds, depending primarily on the ratio between dose and solubility. Non-sink conditions in vivo lead to less than proportional increases of bioavailability for increased doses. This is illustrated in Fig. 21.8, where the fraction of drug absorbed has been simulated by use of an compartmental absorption and intestinal transit model [35] for different doses and for different permeabilities of a low-solubility, aprotic compound. 

To understand the impact of individual processes on the compartmental distribution of DDT, model runs with a non-steady-state, zero-dimensional, multimedia mass balance box model (MPI-MBM) [Lammel (2004)] were conducted in addition to MPI-MCTM experiments. Parameterisations of intra- and intercompartmental mass exchange and conversion process in MPI-MBM are similar to those in MPI-MCTM. A detailed description of differences and a comparison of both models can be found in Lammel et al (2007). The DDT emissions were the global mean temporally varying DDT applications for the years 1950 to 1990. A repeating annual cycle around constant mean temperatures was simulated. Surface and air temperatures differ by 14 K constantly. 

---