Elimination rate constant and

The following data was obtained after the administration of a single 500-mg dose of a drug by slow intravenous infusion. Calculate the AUC, elimination rate constant, and the biological half-life of the drug. 

The elimination rate constant and half-life (h/2), the time taken for the drug concentration present in the circulation to decline to 50 % of the current value, are related by the equation ... 

Single-dose pharmacokinetics including relationship among dose and plasma concentration, absorption rate, total, metabolic and renal clearance, volume of distribution, elimination rate constant and half-life... 

In these equations kei is the elimination rate constant and AUMC is the area under the first moment curve. A treatment of the statistical moment analysis is of course beyond the scope of this chapter and those concepts may not be very intuitive, but AUMC could be thought of, in a simplified way, as a measure of the concentration-time average of the time-concentration profile and AUC as a measure of the concentration average of the profile. Their ratio would yield MRT, a measure of the time average of the profile termed in fact mean residence time. Or, in other words, the time-concentration profile can be considered a statistical distribution curve and the AUC and MRT represent the zero and first moment with the latter being calculated from the ratio of AUMC and AUC. 

Figure 9.3 presents the general relationship between the gill elimination rate constant and Kow and shows that k2 does not vary with Kow for lower Kow chemicals but shows a distinct drop with Kow for higher Kow chemicals. Numerous studies have reported this drop, usually in the form of a log-log relationship. The relationship between k2 and Kow for lower Kow chemicals (Kow < 1,000) rarely has been observed, because bioaccumulation studies... 

Volume of distribution and clearance are both properties of a drug. These two properties determine a drug s elimination rate constant and half-life (Equation 7.12). 

In the absence of concentration-time profiles after IV administration, it is impossible to estimate the actual elimination rate constant, and the interpretation of absorption and elimination rates after SC administration of macromolecules must be done cautiously. It is for this reason surprising that so few published pharmacokinetic studies include IV administration to assess whether or not the macromolecule follows flip-flop pharmacokinetics. 

Fig. 4 A three-dimensional surface plot of WSS versus elimination rate constant and volume of distribution for a two-parameter model.

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... 

FIGURE 3.6 Compartmental analysis for different terms of volume of distribution. (Adapted from Kwon, Y., Handbook of Essential Pharmacokinetics, Pharmacodynamics and Drug Metabolism for Industrial Scientists, Kluwer Academic/Plenum Publishers, New York, 2001. With permission.) (a) Schematic diagram of two-compartment model for compound disposition. Compound is administrated and eliminated from central compartment (compartment 1) and distributes between central compartment and peripheral compartment (compartment 2). Vj and V2 are the apparent volumes of the central and peripheral compartments, respectively. kI0 is the elimination rate constant, and k12 and k21 are the intercompartmental distribution rate constants, (b) Concentration versus time profiles of plasma (—) and peripheral tissue (—) for two-compartmental disposition after IV bolus injection. C0 is the extrapolated concentration at time zero, used for estimation of V, The time of distributional equilibrium is fss. Ydss is a volume distribution value at fss only. Vj, is the volume of distribution value at and after postdistribution equilibrium, which is influenced by relative rates of distribution and elimination, (c) Time-dependent volume of distribution for the corresponding two-compart-mental disposition. Vt is the starting distribution space and has the smallest value. Volume of distribution increases to Vdss at t,s. Volume of distribution further increases with time to Vp at and after postdistribution equilibrium. Vp is influenced by relative rates of distribution and elimination and is not a pure term for volume of distribution. 

Each of the exponential decay terms in the generalized multicompartment models represent a distinct phase or change in shape of the plasma concentration versus time curve. The extra (n+l) exponential term for first-order absorption always has the absorption rate constant (ka) in the exponent, and always represents an absorption phase. The exponential term with the smallest rate constant (A ) always represents the elimination phase, and this rate constant always represents the elimination rate constant and always equals the terminal line slope m= — A J. All other exponential terms represent distinct distribution phases caused by the different rates of distribution to different tissue compartments. 

Where k = elimination rate constant and Vd = apparent volume of distribution... 

Vss is volume of distribution at steady state, F is oral bioavailability, ka is the absorption rate constant, kei is the elimination rate constant and x is the dosing interval. If the units of MEC are mg/mL, expressed as mL/kg, bioavailability F expressed as a fraction, ka and kgi in hours and dose frequency in hours, then the dose will be in units mg/kg/day. 

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... 

Equation 3.8 also permits determination of the elimination rate constant and/or the elimination half life this, however, will require the knowledge of two plasma concentration values and the corresponding time values. One may also employ this equation to determine the time at which a particular plasma concentration value occurs. This is possible if the initial plasma concentration and the elimination half life and/or rate constant are known. 

The data reported in column 7 (i.e. ARE or [(A u)=o — (Au)tl) is plotted against time (data in column 6 of the table) on semilogarithmic paper (Fig. 3.21). The slope of the graph should permit the determination of the elimination rate constant and the intercept on the y-axis represents the value for (Xu) , which, in this example, is equal to the administered dose. Note that, since the drug is assumed to be totally removed in an unchanged form, the elimination rate constant is equal to the excretion rate constant, and the cumulative amount of drug excreted in the urine at time infinity, (Xu) , is equal to the administered dose. 

In Fig. 4.7, please note the differences in the slope of the concentration versus time data, which will be reflected in the elimination rate constant and the elimination half life of the drug. Questions for reflection Is the initial plasma concentration of the drug also affected by the renal insufficiency Will the apparent volume of drug distribution be different in three subjects Will the systemic clearance of this drug be different in each subject Will the area under the plasma concentration (AUC)o be different in each subject ... 

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) ... 

When fitting plasma drug concentration data to the one-compartment extravascular model by non-linear regression, estimates for the elimination rate constant and absorption rate constant from regular and flip-flop approaches will have exactly the same correlation coefficient,... 

Since the apparent volume of distribution, elimination rate constant, and elimination half... 

Equations 11.13 and 11.14 permit determination of the minimum or trough plasma concentration at steady state. A careful examination of the equation clearly suggests that the minimum or trough plasma concentration for a dmg is influenced by the initial plasma concentration, the elimination rate constant and, more importantly, the dosing interval. Since the administered dose is identical and the elimination rate constant is a constant, the minimum plasma concentration at steady state is influenced only by the dosing interval. 

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