Drugs first-order

The first-order rate constant for the decomposition of a certain drug at 25°C is 0.215 month1. 

Drug elimination may not be first order at high doses due to saturation of the capacity of the elimination processes. When this occurs, a reduction in the slope of the elimination curve is observed since elimination is governed by the relationship Vmax/(Km- -[conc]), where Vmax is the maximal rate of elimination, Km is the concentration at which the process runs at half maximal speed, and [cone] is the concentration of the drug. However, once the concentration falls below saturating levels first-order kinetics prevail. Once the saturating levels of drugs fall to ones eliminated via first-order kinetics, the half time can be measured from the linear portion of the In pt versus time relationship. Most elimination processes can be estimated by a one compartment model. This compartment can... 

There are instances where the observable kinetics of elimination clearly are not due to first-order exit from a single compartment. For example, a steep curve relating drug concentration and time may indicate a two-compart-ment system in which the drug exits in two phases, one fast... 

First order kinetics describes the most common time course of drug elimination. The amount eliminated within a time-interval is proportionate to the drug concentration in the blood. 

If the drug is administered by a constant infusion rate (IR), the curve follows an unsteady function with zero-order kinetics (AClAt = const.) before the infusion is stopped (t < Tinfus) and first-order kinetics after cessation of infusion. Zero-order kinetics frequently can also be observed with diug absoiption where (KOabs = DR.) and (Tabs = Tinfus) hold true. 

Strobel et al. (101) reported a unique approach to delivery of anticancer agents from lactide/glycolide polymers. The concept is based on the combination of misonidazole or adriamycin-releasing devices with radiation therapy or hyperthermia. Prototype devices consisted of orthodontic wire or sutures dip-coated with drug and polymeric excipient. The device was designed to be inserted through a catheter directly into a brain tumor. In vitro release studies showed the expected first-order release kinetics on the monolithic devices. 

Equation (3) is in the form of a differential equation describing a first-order kinetic process, and, as a result, drug absorption generally adheres to first-order kinetics. The rate of absorption should increase directly with an increase in drug concentration in the GI fluids. 

It is far more difficult to establish the mechanism(s) of drug absorption in humans. Most investigators analyze drug absorption data in humans (from blood or urine data) by assuming first-order absorption kinetics. For the most part this assumption seems quite... 

Most drugs appear to be absorbed in humans by passive diffusion (linear or first-order kinetics). The predominant pathway taken by most drugs is through the epithelial cell, the transcellular route. It is this route that requires the compound to have a reasonable K0/w... 

The impact of presystemic elimination may be clearly understood by considering the following relationships among the several steps involved in making the drug available to the systemic circulation. The significance of this relationship is its multiplicative nature, since most of the processes are sequential. These relationships assume linear or first-order kinetics (i.e., there is no nonlinearity or saturation effects). 

On some occasions, the body does not behave as a single homogeneous compartment, and multicompartment pharmacokinetics are required to describe the time course of drug concentrations. In other instances certain pharmacokinetic processes may not obey first-order kinetics and saturable or nonlinear models may be required. Additionally, advanced pharmacokinetic analyses require the use of various computer programs, such as those listed on the website http //www.boomer.org/pkin/soft.html. 

Fortunately, most ADME processes behave as pseudo-first-order processes—not because they are so simple, but because everything except the drug concentration is constant. For example, the elimination of a drug from the body may be written as follows ... 

If everything except the concentration of drug in the body is constant, the elimination of the drug will be a pseudo-first-order process. This may seem to be a drastic oversimplification, but most in vivo drug processes, in fact, behave as pseudo-first-order processes. 

For most practical purposes, a first-order process may be deemed complete if it is 95% or more complete. Table 1 shows that five half-lives must elapse to reach this point. Thus the elimination of a drug from the body may be considered to be complete after five half-lives have elapsed (i.e., 97% completion). This principle becomes important, for example, in crossover bioavailability studies in which the subjects must be rested for sufficient time between each drug administration to ensure that washout is complete. 

III. FIRST-ORDER PHARMACOKINETICS DRUG ELIMINATION FOLLOWING RAPID INTRAVENOUS INJECTION... 

It was mentioned previously that drug elimination from the body most often displays the characteristics of a first-order process. Thus, if a drug is administered by rapid intravenous (IV) injection, after mixing with the body fluids its rate of elimination from the body is proportional to the amount remaining in the body. 

Since all the kinetic characteristics of the disappearance of a drug from plasma are the same as those for the pseudo-first-order disappearance of a substance from a solution by hydrolysis, the same working equations [Eqs. (11) and (13)] and the same approach to solving problems can be used. 

Db = drug in the body De = eliminated drug ka = first-order absorption rate constant kei = overall elimination rate constant... 

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. 

Fig. 10 Semilogarithmic plot of observed plasma concentrations (crosses) and residuals (circles) versus time for an orally administered drug absorbed by a first-order process.

The Wagner-Nelson method of calculation does not require a model assumption concerning the absorption process. It does require the assumption that (a) the body behaves as a single homogeneous compartment and (b) drug elimination obeys first-order kinetics. The working equations for this calculation are developed next. 

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