Plotting drug concentration versus time

A semilogarithmic plot of plasma concentration against time can be used to obtain important pharmacokinetics parameters such as the elimination half life, the elimination rate constant and the apparent volume of drug distribution. Table 3.2 gives a set of such data Fig. 3.11 shows the data plotted on rectilinear co-ordinates and 

Determination of the elimination half life and the initial plasma concentration 

From the semilogarithmic plot (Fig. 3.12), the elimination half life and the initial plasma concentration can be obtained) 1.3h and 63pgmL , respectively. 

Equation 3.11 gives the relationship of the apparent volume of distribution with dose and plasma concentration  

Equation 3.12 gives the relationship of the overall elimination rate constant with the half life  

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Thus, %F is defined as the area under the curve normalized for administered dose. Blood drug concentration is affected by the dynamics of dissolution, solubility, absorption, metabolism, distribution, and elimination. In addition to %F, other pharmacokinetic parameters are derived from the drug concentration versus time plots. These include the terms to describe the compound s absorption, distribution, metabolism and excretion, but they are dependent to some degree on the route of administration of the drug. For instance, if the drug is administered by the intravenous route it will undergo rapid distribution into the tissues, including those tissues that are responsible for its elimination. 

Plasma After drawing and labelling the axes, plot the concentration versus time curve for an orally administered drug. Label this curve plasma to show how the concentration rises and falls with time following an oral dose. 

A semi-log plot of drug concentration versus time will no longer be linear as the drug has two possible paths to move along, each with their own associated rate constants. 

Area under curve (AUC] The total area under the plot-of-drug concentration versus time following either a single dose or multiple doses of a specific drug product (e.g., formulation) in a specific patient by a specific route of administration. 

E. A plot of drug concentration versus, time is a straight line. 

D. show a plot of drug concentration versus time that is linear. 

Half-life (t) is usually defined as the time required for the amount of drug in blood to decline to one half of a measured value. Figure 33-8 demonstrates how the half-fife can be rapidly determined from a semilog plot of drug concentration versus time. Two or more successive concentrations collected at times fi and are required for the estimate of k used in the calculation of half-life... 

Figure 4.3. Plot of drug concentration versus time for single and multiple doses.

Fig. 9.31. Typical semilogarithmic plot of drug concentration versus time profile in plasma following the administration of a drug by an extravascular route. The dashed line represents the feathered line used to obtain the absorption rate constant (K ).

Finally, one can plot plasma drug concentrations versus time on semilogarithmic paper. This has the effect of linearizing Eq. 2.4. The slope equals —lC/2.303, but the y-axis intercept now equals (Cp)o, since Cp, rather than log Cp values were plotted (Fig. 2. Id). 

The projections of this plot against each coordinate plane produces the three plots plasma drug concentration versus time, drug effect versus time and drug effect versus plasma drug concentration (Fig. 17.5). 

I represents the y-axis intercept of a plasma drug concentration versus time plot. By Eq. A.15,... 

Normally, the plasma concentration is used as a measure of the amount of drug in the body, and a plot of plasma concentration versus time has the same characteristics as the plot in Fig. 1. A semilogarithmic... 

Fig. 4 Semilogarithmic plot of plasma concentration versus time for a drug administered by rapid intravenous injection.

For drugs that are both metabolized and excreted unchanged, semilogarithmic plots of plasma concentrations versus time will provide values of kei. 

Equation (35) describes the line in Fig. 10, which is a semilog plot of Cp versus time for an orally administered drug absorbed by a first-order process. The plot begins as a rising curve and becomes a straight line with a negative slope after 6 hours. This behavior is the result of the biexponential nature of Eq. (35). Up to 6 hours, both the absorption process [exp(—kat) and the elimination process [exp( keil)] influence the plasma concentration. After 6 hours, only the elimination process influences the plasma concentration. 

Thus after 6 hours the semilog plot of Cp versus time shown in Fig. 10 becomes a straight line and kei can be determined from the slope. Therefore, the overall elimination rate constant for a drug may be accurately determined from the tail of a semilog plot of plasma concentration versus time following extravascular administration if ka is at least five times larger than kei. 

The rate of appearance of drug in the plasma Cp is directly proportional to the concentration of drug at the site of absorption (C slte 0f absorption)- Like all first-order rate constants, the units of the absorption rate constant ka are 1/time. A plot of drug amount versus time is shown in Fig. 1.7. 

Half-life can be readily determined from a plot of log plasma concentration versus time and was for many years considered to be the most important characteristic of a drug. Early studies examining drug disposition in disease states were compromised, by a reliance on half-life as a sole measure of disposition changes. It is now appreciated that half-life is a secondary, derived parameter that relates to and depends on the primary parameters of clearance (CL) and volume of distribution (E) according to the following relationship in Eq. (25) ... 

Fig. 9.37. Plots of drug concentration ([jg/mL ) and drug concentration x time ((jg/ml /hr o) versus time during and after 1 hour of a constant-rate infusion. The area under the concentration versus time plot to infinity is AUC the area under the concentration x time versus time plot to infinity is AUMC. (From Gibaldi M. Biopharmaceutics and Clinical Pharmacokinetics, 4th Ed. Philadelphia Lea and Febiger, 1991 with permission.)...

In relation to drug residues, a pharmacokinetic property of major significance is the very late terminal elimination half-life (see Sections 2.3.1 and 2.7.1). For many drug classes, a semi-logarithmic plot of plasma concentration versus time, after intravenous dosing, reveals a... 

Figure 1.3 A typical plasma concentration versus time plot (rectilinear paper) following the administration of a dose of a drug by an intravascular route.

Figure 1.4 A typical plot (rectilinear paper) of plasma concentration versus time following the (oral) administration of an identical dose of a drug via identical dosage form but different formulations. MTC, minimum toxic concentration MEC, minimum effective concentration.

Please note that, in order to determine the apparent volume of distribution of a drug, it is necessary to have plasma/serum concentration versus time data. Once such data are obtained following the administration of a single dose of a drug intravenously, one may prepare a plasma concentration (Cp) versus time plot on semilogarithmic paper, as shown in Fig. 3.7. 

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.)...

In this question, plasma concentration versus time data is provided following the administration of two different doses of a drug (cinoxacin Cinobac). Because of the assumption of the first-order process and passive diffusion, one would expect the plasma concentration of a drug at any time to be directly proportional to the dose administered however, the fundamental pharmacokinetic parameters of a dmg will remain unaffected by the administered dose. We plotted... 

This question involves two different doses of an identical drug (promethazine) in an identical dosage form (tablet), via an identical route of administration (oral) of an identical formulation (made by the same manufacturer). Plasma concentration versus time data were plotted on suitable semilogarithmic graph paper. As mentioned above, greater variation can occur in the values in parts a-d because of the technique employed. This variation, in turn, will be reflected in the answers for the peak time, peak plasma concentration and the intercept of the plasma concentration versus time profile. 

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