Subject zero order

Early work of Dhar established that oxidation of oxalic acid by chromic acid occurs readily, but some of his kinetic data are unreliable as the substrate itself acted as the source of hydrogen ions. The reaction is first-order in oxidant and is subject to strong manganous ion catalysis (as opposed to the customary retardation), the catalysed reaction being zero-order in chromic acid. This observation is related to those found in the manganous-ion catalysed oxidations of several organic compounds discussed at the end of this section. 

In the case of gastric retentive dosage forms, zero-order delivery may not be as useful. In studying the patient population, certain subjects may show rapid gastric emptying in the fed mode or may be noncompliant and take their medication while fasting, although intended for fed... 

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).

One of the very first kinetic examples of this catalyzed prototropy was found in the halogenation of acetone. In polar solvents, it is found that the rate of halogenation of acetone is first-order in acetone, zero-order in halogen, X2, and subject to general acid-base catalysis ... 

Alcohol is subject to first-order kinetics with a t) of about one hour at plasma concentrations below 10 mg/dl [attained after drinking about two-thirds of a unit (glass) of wine or beer]. Above this concentration the main enzyme (alcohol dehydrogenase) that converts the alcohol into acetaldehyde approaches and then reaches saturation, at which point alcohol metabolism caimot proceed any faster. Thus if the subject continues to drink, the blood alcohol concentration rises disproportionately, for the rate of metabolism remains the same (at about 10 ml or 8 g/h for a 70 kg man), i.e. a constant amount is metabolised in unit time, and alcohol shows zero-order kinetics. 

When a drug is subject to first-order kinetics and by definition the rate of elimination is proportional to plasma concentration, then the t) is a constant characteristic, i.e. a constant value can be quoted throughout the plasma concentration range (accepting that there will be variation in t) between individuals), and this is convenient. If the rate of a process, e.g. removal from the plasma by metabolism, is not directly proportional to plasma concentration, then the t) cannot be constant. Consequently, when a drug exhibits zero-order elimination kinetics no single value for its t] can be quoted for, in fact, t) decreases as plasma concentration falls and the calculations on elimination and dosing that are so easy with first-order elimination (see below) become too complicated to be of much practical use. 

The elimination rate for zero-order processes may also be treated as a maximal rate of reaction (Fmax) and thus this type of data may be subject to ordinary Michaelis-Menten analysis (see further, below). Note that first-order elimination curves are so common that drug disappearance curves are routinely analyzed as semi-logarithmic plots (which linearizes the curve). The literature is sometimes ambiguous in its use of the term linear data , authors may or may not assume that the semi-logarithmic transformation is to be taken as read. 

The plasma drug profiles in 50 subjects, following oral administration of the drug X and assuming a zero-order absorption process, are plotted in Figure 13.3. Corresponding NONMEM control file and data set are in Appendix 13.2. 

FIGURE 133 Plot of simulated plasma concentrations of drug X in 50 subjects, following a single oral dose, assuming a zero-order absorption type. Normal left panel) and semilog right panel) scale. Thick line represents population predictions for a typical subject. 

A number of studies have explored ways in which partial vapor pressures may be obtained using TGA data, thereby allowing both prediction of vapor pressure under a range of circumstances and calculation of the constants associated with the approaches described previously. In particular, Price and Hawkins (12) have argued that the rate of mass loss for vaporization and sublimation within a TGA should be a zero-order process, and hence should be constant for any given temperature, subject to the important condition that the available surface area also remains constant. This means that the value of v from Equation 6.4 should be easily calculated from the TGA data. If one performs this experiment for materials with known vapor pressure and temperature relationships (the authors used discs of acetamide, benzoic acid, benzophenone, and phenanthrene), then the constant k for the given set of TGA experimental conditions may be found. Once this parameter is known, the vapor pressure may be assessed for an unknown material in the same manner. 

Other initiation and zip orders have been evaluated. All non-steady-state models appear to be markedly superior to models that invoke the steady-state hypothesis, but none is appreciably better than the simple assumption of first order initiation and zero order zip. The derivation and evaluation of other non-steady-state models will be the subject of a later publication. 

The Monsanto catalyst system has been the subject of numerous studies (for leading references see [6-12,16,18]). The rate of the overall carbonylation process is zero order in each of the reactants (MeOH and CO) but first order in the rhodium catalyst and in the methyl iodide cocatalyst,... 

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