Plasma concentration versus time plots determination

In the total plasma response approach, the bioavailability of a compound is determined by measuring its plasma concentration at different times (up to weeks) after single or long-term ingestion of the compound from supplements or food sources. Generally, a plasma concentration-versus-time plot is generated, from which is determined the area-under-curve (AUC) value used as an indicator of the absorption of the componnd. Here, the term relative bioavailability is more appropriate since AUC valnes of two or more treatments are usually compared. This is in contrast to absolnte bioavailability for which the AUC value of the orally administered componnd is compared to that obtained with intravenous administration taken as a reference (100% absorption). 

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 AUC is determined by plotting the plasma concentration versus time on normal rectilinear graph paper, dividing the area up into trapezoids, and calculating the area of each trapezoid (Fig. 3.24). The total area is then the sum of the individual areas. Although the curve theoretically will never meet the x axis, the area from the last plasma level point to infinity may be determined from Ct/ke. The units are mgL 1hr. 

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) ... 

Pharmacokinetic Analysis. Standard noncompartmental analyses were conducted to assess ATI and ATF pharmacokinetics using WinNonlin software (v. 2.1) (Pharsight, Mountain View, CA). The areas under the plasma concentration versus time curve from time zero to inhnity (AUCint) were determined via the log-linear trapezoidal method. The terminal half-life was determined from the relationship of ti/2 = In 2/, where k is the negative slope of the terminal phase of the InC versus time plot. Systemic clearance (CL) was estimated by dividing the administered dose by AUCint. The volume of distribution at steady state (Vss) was determined by the product of clearance and the mean residence time. 

The elimination half life of a dmg may be determined by employing Eq. 3.12, provided that the value of the elimination rate constant is known or provided. Alternatively, the elimination half life may be obtained from the semilogarithmic plot of plasma concentration versus time data, as described in Fig. 3.10. 

We plotted plasma concentration versus time data on a two-cycle semilogarithmic graph paper and then determined the following ... 

In this problem, in addition to determining the pharmacokinetic parameters such as the elimination half life, elimination rate constant and the apparent volume of distribution of the drug, the systemic clearance of the drug and the area under the plasma concentration time curve for the administered dose of the drug are required. The plot of plasma concentration versus time data was made on suitable semilogarithmic paper. From the graph, the following can be determined (for healthy subjects) ... 

A one-compartment model (Figure 6.15) is based on a single compartment— here, the plasma—also referred to as the central compartment. A first-order rate constant kg determines how fast the drug is absorbed into the bloodstream, while the first-order elimination rate constant kei describes the speed at which the drug is removed. A logarithmic plot of plasma concentration versus time is linear with a slope of - kei/2.303. The plasma concentration as a function of time is described by the relationship ... 

In addition to the elimination rate constant, the half-life (T/i) another important parameter that characterizes the time-course of chemical compounds in the body. The elimination half-life (t-1/2) is the time to reduce the concentration of a chemical in plasma to half of its original level. The relationship of half-life to the elimination rate constant is ti/2 = 0.693/ki,i and, therefore, the half-life of a chemical compound can be determined after the determination of k j from the slope of the line. The half-life can also be determined through visual inspection from the log C versus time plot (Fig. 5.40). For compounds that are eliminated through first-order kinetics, the time required for the plasma concentration to be decreased by one half is constant. It is impottant to understand that the half-life of chemicals that are eliminated by first-order kinetics is independent of dose. ... 

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 support of inhalation studies, blood samples are taken after a 4- to 6-hour whole-body or nose-only exposure period. The steady-state plasma concentration and the elimination rate are determined. The steady-state concentrations are plotted versus exposure concentration to make the determination of dose proportionality. A kinetic model is developed and used to predict steady-state concentrations and the time to reach steady state. 

Elimination parameters are determined by linear regression analysis of the measured plasma concentration data falling on the terminal line. As always, the first step is to calculate the natural logarithm of each of the measured plasma concentration values. The values of In(C ) are then plotted versus time (t). If the plot shows later points falling near a straight terminal line with no early points above the terminal line, then the data can be well represented by the one-compartment first-order absorption model. As with previous one-compartment models, early high points above the terminal line indicate that the one-compartment model is not the best PK model for the data, and erratic late data points could mean the values are unreliable, as illustrated in Figure 10.47. 

Estimation of multicompartment model parameters from measured plasma samples is very similar to the procedures described previously for the two-compartment first-order absorption model. The first step is to calculate bi(C ) for each of the measured plasma sample concentrations. The values of In(C ) are then plotted versus time (t), and the points on the terminal line are identified. Linear regression analysis of the terminal line provides values for B (B = c ) and In = —m). The first residual (/ i) values are then calculated as the difference between the measured plasma concentrations and the terminal line for points not used on the terminal line. A plot of ln(i i) versus t is then employed to identify points on the next terminal line, with linear regression analysis of this line used to determine and X -. Successive method of residuals analyses are then used to calculate the remaining B and A, values, with linear regression of the n-1 residual (Rn-i) values providing the values of Bi and Aj. If a first-order absorption model is being used, then one more set of residuals (R ) are calculated, and the linear regression analysis of these residuals then provides and kg. This type of analysis is typically performed by specialized PK software when the model contains more than two compartments. 

Figure 3.10 Semilogarithmic plot of plasma concentration (Cp) versus time following administration of the drug prednisolone by intravenous bolus injection. Such a plot permits the determination of the elimination half life (ti/2) and the elimination rate constant (k). (Cp)o, initial plasma concentration.

The kinetics of the polymerization of pyrrole can be followed by measuring the disappearance of the reactants. Pyrrole concentrations can be determined by gas chromatography [10]. The depletion of iron can be followed by the titration of the iron(III) chloride with a complexing agent, and the disappearance of the sulfur-containing doping agents can be determined by inductively coupled plasma (ICP) [47]. Experiments reveal that the reaction follows second-order autocatalytic kinetics [ 10]. A plot of the concentrations of pyrrole monomer (surface and no surface) versus time at room temperature is shown in Fig. 35.5. The surface resistance of the polypyrrole-coated textiles can be controlled by... 

In Eq. (3.1), C is the concentration of drug in the plasma at time t, C0 is the concentration of drug in the plasma extrapolated to t = 0, and k is the first-order rate constant. A semilogarithmic plot of the log C versus t yields a straight line, where the slope of the line is given by -hi2.303 and Co is given by the intercept of the y-axis (Fig. 3.2). The first-order rate constant, k, can be determined from the slope of the line or more simply from the relationship stated in Eq. (3.2). 

Standard curves were constructed by plotting the change in absorbance with time (dA/dt) versus concentration of ATI or ATF. Standards for the assay were prepared by dilution of stock solutions of ATI or ATF to the appropriate concentrations (0,25,50,100,175, and 250ng/mL for ATI 0,5,10,20,50, and lOOng/mL for ATF) with PBS (pH 7.4), with the addition of 1% (v/v) blank rat plasma. Assays were validated with respect to precision and accuracy, by analysis of QC samples at 25,100,250ng/ml for ATI and 5,20, lOOng/ml for ATF, respectively. Intra-assay and inter-assay variability were determined through the analysis of QC samples. 

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