Intravenous bolus administration one-compartment model

Upon completion of ifiis chapter, you will have the ability to  

A drug is administered as an injection of a sterile solution formulation. The volume and the concentration of the administered solution must be known in order to calculate the administered dose. For example, five milliliters (5 ml) of a 2% w/v solution will contain 100 mg of a drug (dose). There are several important points to note. 

This route of administration ensures that the entire administered dose reaches the general circulation. 

The desired drug concentration in the blood is promptly attained. 

One must be extremely careful in calculating doses or measuring solutions because of the danger of adverse or toxic effects. 

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FIGURE 10.1 Fit obtained using a one-compartment model (see Equation 10.6) to fit plasma concentration-vs-time data observed following intravenous bolus administration of a drug designates the actual measured concentrations and Cp-g represents the concentrations predicted by the pharmacokinetic model. (Adapted from Grasela XH Jr, Sheiner LB. J Pliarmacokinet Biopharm 1991 19(suppl) 25S-36S.)... 

FIGURE 10.2 Fit obtained using a one-compartment model to fit plasma concentration-vs-time data observed following intravenous bolus administration of a drug. Each panel represents an individual patient. 

FIGURE 10.4 Grapliical illustration of the statistical model used in NONMEM for the special case of a one-compartment model following intravenous bolus administration of a drug. , patient / , patient k. (Adapted from Vozeh S et al. Eur J Clin Pliarmacol 1982 23 445-51.)... 

Figure 4.6 Application of the trapezoidal rule to determine the area under the plasma concentration (Cp) versus time curve (AUC). (Rectilinear plot of plasma or serum concentration versus time following the administration of an intravenous bolus of a drug fitting a one-compartment model.)...

As for the intravenous bolus, above, the drug fits a one-compartment model. Figure 4.8 is a semilogarithmic plot of plasma concentration against time following the administration of an identical extravascular dose of a drug to two subjects with different degrees of renal impairment. 

Table Pl.l gives plasma drug concentrations (Cp) obtained following an intravenous bolus administration of a 250 mg dose of a drug that exhibited the characteristics of a one-compartment model and was eliminated exclusively by urinary excretion. Plot the data and, using the plot, determine the following.

This problem set will provide you with the plasma concentration versus time data (questions 1, 2 and 4) as well as urinary data (questions 3 and 5), following the intravenous bolus administration of a drug that follows the first-order process and exhibits the characteristics of a one-compartment model. The following are our answers to these five questions. Please note that your answers may differ from these owing to the techniques employed in obtaining the best fitting straight line for the data provided. These differences will, therefore, be reflected in the subsequent answers. 

From our earlier discussion of intravenous bolus administration (Ch. 3, for the one-compartment model) we know that, for intravenously administered drug. 

The value of (AUC)o can be computed by using the trapezoidal rule (Ch. 4) (Fig. 4.6). It is also important to note that Eq. 7.15 is applicable only for a one-compartment model following oral or intravenous bolus administration. 

One method to obtain initial estimates is linearization of the problem. For example, the 1-compartment model with bolus intravenous administration can be reformulated to a linear problem by taking the log-transform on both sides of the equation. This is a trivial example, but is often reported in texts on nonlinear regression. Another commonly used method is by eyeballing the data. For example, in an Emax model, Emax can be started at the maximal of all the observed effect values. EC50 can be started at the middle of the range of concentration values. Alternatively, the data can be plot-... 

Tse and Szeto (1982) reported on the bioavailability of theophylline following single intravenous bolus and oral doses in beagle dogs (Table P3.1). Plasma theophylline concentrations after intravenous and oral administration were described by a one-compartment open model. The doses administered were as follows ... 

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