Modeling one compartment

In the pharmacodynamic model, the drug concentration at the receptor site is proportional to the drug concentration in the plasma, regardless of the pharmacokinetic model (one compartment or multicompartment), and the interaction between the drug and receptor is directly and rapidly reversible after drug administration. 

Ette (1) provides an example of the application of bootstrapping to PMM budding, specifically to a population pharmacokinetic (PPK) model. In this study it was desired that the deterministic model (one-compartment versus two-compartment) and the covariates for inclusion be known with a high degree of certainty (1, 3). 

Distributed-parameter skin model -----One-compartment skin model... 

Absorption, distribution, biotransformation, and excretion of chemical compounds have been discussed as separate phenomena. In reality all these processes occur simultaneously, and are integrated processes, i.e., they all affect each other. In order to understand the movements of chemicals in the body, and for the delineation of the duration of action of a chemical m the organism, it is important to be able to quantify these toxicokinetic phases. For this purpose various models are used, of which the most widely utilized are the one-compartment, two-compartment, and various physiologically based pharmacokinetic models. These models resemble models used in ventilation engineering to characterize air exchange. 

In a two-compartment model, /3 is equivalent to k in the one-compartment model. Therefore, the terminal half-life for the elimination of a chemical compound following two-compartment model elimination can be calculated from the equation (i = 0.693/ti/i ... 

Drug elimination may not be first order at high doses due to saturation of the capacity of the elimination processes. When this occurs, a reduction in the slope of the elimination curve is observed since elimination is governed by the relationship Vmax/(Km- -[conc]), where Vmax is the maximal rate of elimination, Km is the concentration at which the process runs at half maximal speed, and [cone] is the concentration of the drug. However, once the concentration falls below saturating levels first-order kinetics prevail. Once the saturating levels of drugs fall to ones eliminated via first-order kinetics, the half time can be measured from the linear portion of the In pt versus time relationship. Most elimination processes can be estimated by a one compartment model. This compartment can... 

In this section we describe a cellular automata model of a semipermeable membrane separating two compartments [5]. A solute in one compartment has varied parameters to reflect its relative polarity or lipophilicity. The passage of this solute into and through the membrane is observed, as this property is varied. 

This application is designed to model the influence of various concentrations of a solute near one edge of the membrane, on the diffusion of water through the membrane. Specifically we are interested in determining whether the model reveals a difference in the flow of water out of one compartment relative to the other. It is well known that if a semipermeable membrane is impervious to a solute on one side of a membrane, a greater flow of water from the other side will occur. This is a model of the osmotic effect, the flow of water through the... 

Fig. 39.4. (a) One-compartment open model with single-dose intravenous injection of a dose D. The transfer constant of elimination (excretion and metabolism) is kp - (b) Time course of the plasma concentration Cp and of the contents in the elimination pool Xp. 

Fig. 39.6. (a) Time courses of plasma concentration Cp in the one-compartment open model for intravenous injection, with different contingencies for the transfer constant of elimination kfe and the volume of distribution Vp. (b) Time courses of plasma concentration Cp as in panel (a) on semilogarithmic plots. 

The synthetic data have been derived from a theoretical one-compartment model with the following settings of the parameters ... 

One-compartment open model for continuous intravenous infusion... 

In the previous discussion of the one- and two-compartment models we have loaded the system with a single-dose D at time zero, and subsequently we observed its transient response until a steady state was reached. It has been shown that an analysis of the response in the central plasma compartment allows to estimate the transfer constants of the system. Once the transfer constants have been established, it is possible to study the behaviour of the model with different types of input functions. The case when the input is delivered at a constant rate during a certain time interval is of special importance. It applies when a drug is delivered by continuous intravenous infusion. We assume that an amount Z) of a drug is delivered during the time of infusion x at a constant rate (Fig. 39.10). The first part of the mass balance differential equation for this one-compartment open system, for times t between 0 and x, is given by ... 

When infusion stops at time x, the plasma concentration Cp(x) decays exponentially according to the solution of the one-compartment open model in eq. 

We consider again the pharmacokinetic parameters of the one-compartment model for a single intravenous injection (eq. (39.6)). 

This model is an extension of the one-compartment model for intravenous injection (Section 39.1.1) which is now provided with a peripheral buffering compartment which exchanges with the central plasma compartment. Elimination occurs via the central compartment (Fig. 39.12). The model requires the estimation of the plasma volume of distribution and three transfer constants, namely for... 

A random noise with standard deviation of 0.4 pg 1 has been added to the theoretical values in order to produce a realistic example. The specifications of the model are in part the same as those used for the one-compartment models which have been discussed above. The major distinction between this model and the... 

In the case of a one-compartment open model with single-dose intravenous administration, the mean residence time is simply the inverse of the elimination transfer constant kp, since according to the above definition we obtain ... 

The mean residence time MRT can thus be defined as the time it takes for a single intravenous dose to be reduced to 36.8% in a one-compartment open model. This follows from the property derived above in eq. (39.105) and from eq. (39.5) ... 

In the special case of a one-compartment open model, it can easily be shown that the steady-state volume is identical to the plasma volume Vp which has been defined before in Section 39.1.1 (eq. (39.12)) ... 

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