First-order elimination rate constant

In Eq. (3.4), doseiv is the amount of drug administered intravenously, AUC is total area under the drug concentration-time curve, and k is the first-order elimination rate constant... 

First-order elimination rate constant K and half-life f1/2... 

The first-order elimination rate constant K can be determined as shown in Eq. (1.4) and has units of 1/time. The larger the value of K, the more rapidly elimination occurs. Once K has been determined, then calculating the half-life t1/2 is straightforward (Eq. 1.5). 

Fig. 9. Semilogarithmic plots of plasma concentrations versus time for 3 doses of salicylate administered to the same subject, illustrating capacity-limited elimination. At low plasma concentrations, parallel straight lines are obtained from which the first-order elimination rate constant can be estimated. As long as concentrations remain sufficiently high to saturate the process, elimination follows zero-order kinetics (C. A. M. van Ginneken et al., J. Pharmacokinet. Biopharm., 1974,2, 395-415).

FIGURE 4.9 Disposition model representing the elimination of a unit impulse drug dose (Hq = 1) from a single body compartment. Drug in this compartment (H) is removed as specified by the first-order elimination rate constant k. 

This equation describes the typical time course of amount of drug in the body (A) as a function of initial dose, time (t), and the first-order elimination rate constant (k). As was described by Equation 2.14, this rate constant equals the ratio of the elimination clearance (CLe) relative to the distribution volume of the drug ( d)/ so fhaf Equation 10.1 can then be expressed in terms of concentration in plasma (C ). 

When the drug is administered by an extravascular route, correction for dose must be made in the systemic availability (F) and the apparent first-order elimination rate constant, obtained from the late decline phase of the curve, should be substituted for (3 in the area method equation. 

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... 

Using the same assumptions, the first-order elimination rate constant can be determined. Referring to Figure 33-8, note that the relation between Cf and time is a natural logarithmic function where... 

Overall First-Order Elimination Rate Constant... 

If the elimination rate, metabolic rate, and excretion rate all follow first-order (or linear) kinetics, then the overall first-order elimination rate constant (k) can be written as... 

Lag coefficient for particle in a pore Bessel function of the first kind of order 0 Mass flux of component A (mg/cm s) in a binary mixture with respect to a coordinate system that is moving with the mass average velocity of the mixture Enhanced friction for particle within a pore Equilibrium partition coefficient First-order elimination rate constant (s )... 

The first order elimination rate constant [K] is a constant, as the name implies. 

Figure 3.1 Scheme and setup of one-compartment intravenous bolus model. X, mass (amount) of drug in the blood/body at time, t X mass (amount) of unchanged drug in the urine at time, t K, first-order elimination rate constant. 

Therefore, at ti the fraction of all the drug initially present that will be eliminated over 1 s is (0.05 X Cpi pg)/(1000 X Cpi pg), which is 0.00005. A similar calculation for time t2 gives the same value for this fraction. Since t2 is an appreciable time later than ti, we can conclude that this fraction is constant over time. It turns out that 0.00005 s is the value of the first-order elimination rate constant, K, for this problem. This can be confirmed by dividing clearance by V ... 

Figure 6.3 Absorption of a one-compartment drug with first-order elimination, where is the mass or amount of absorbable drug remaining in the gut, or at the site of administration, attimet (i.e. drug available for absorption at time Xisthe mass or amount of drug in the blood at time, f X is the mass or amount of drug excreted unchanged in the urine at time, t Ka is the first-order absorption rate constant (h or min j and /C(or /Cei) is the first-order elimination rate constant (h or min ).

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