Concentration-time relation

It can readily be shown (Problem 87) that the concentration-time relation for a zero-order reaction is... 

Ideally, if mouse experiments are to be vised to estimate the rate of induction of gene or chromosomal mutations, chemicals should be tested at enough doses to establish a dose-response curve. However, if the purpose is simply to confirm that a chemical is mutagenic in a mammal, then a single positive result at a single dose is sufficient. A large dose (close to the maximum that is tolerated by the animal) can be given, and the concentration-time relations can be adjusted so that other toxicity does not unduly influence the mutant yield. 

Equation (III.2.5), which expresses the concentration-time relation, is rather difficult to apply experimentally, since it requires a previous knowledge of ki and 2, or at least their ratio. Although we shall say more about such problems in Chapter IV, it is well to consider here the relation of the above rate law to this eventual equilibrium reached in these systems. 

Figure 21-6. Experimental setup of ECP (a), MDM (b), and ADM (c) method for the determination of adsorption isotherms. The concentration-time relation of the dispersed taU in the ECP approach (a) is completely defined by the course of the adsorption isotherm, as can be visuahzed by the injection of increasing samples amounts. Solvent injections at defined concentrations will result in pulses in the MDM approach (b) which are linked to the adsorption isotherms. Although very precise during application of the ADM method, the data points of the adsorption isotherms (c) have to be measnred individually.

The basic differential equations and the concentration-time relations for parallel reactions for longitudinal and backmixing reactions are shown in Table 3-3, and the corresponding product-distribution equations are shown in Table 3-4. It can be seen from these equations that backmixing does not effect the product distribution for parallel reactions of the same order. 

Toxicity is related to dose and degree of hazard associated with a material. Dose is time- and duration-dependent, in that dose is a function of exposure (concentration) times duration. 

Kinetic studies at several temperatures followed by application of the Arrhenius equation as described constitutes the usual procedure for the measurement of activation parameters, but other methods have been described. Bunce et al. eliminate the rate constant between the Arrhenius equation and the integrated rate equation, obtaining an equation relating concentration to time and temperature. This is analyzed by nonlinear regression to extract the activation energy. Another approach is to program temperature as a function of time and to analyze the concentration-time data for the activation energy. This nonisothermal method is attractive because it is efficient, but its use is not widespread. ... 

Therapeutic diug monitoring by measurement of concentrations at a defined time related to drug dosing. 

There have been few satisfactory demonstrations that decompositions of hydrides, carbides and nitrides proceed by interface reactions, i.e. either nucleation and growth or contracting volume mechanisms. Kinetic studies have not usually been supplemented by microscopic observations and this approach is not easily applied to carbides, where the product is not volatile. The existence of a sigmoid a—time relation is not, by itself, a proof of the occurrence of a nucleation and growth process since an initial slow, or very slow, process may represent the generation of an active surface, e.g. poison removal, or the production of an equilibrium concentration of adsorbed intermediate. The reactions included below are, therefore, tentative classifications based on kinetic indications of interface-type processes, though in most instances this mechanistic interpretation would benefit from more direct experimental support. 

This chapter takes up three aspects of kinetics relating to reaction schemes with intermediates. In the first, several schemes for reactions that proceed by two or more steps are presented, with the initial emphasis being on those whose differential rate equations can be solved exactly. This solution gives mathematically rigorous expressions for the concentration-time dependences. The second situation consists of the group referred to before, in which an approximate solution—the steady-state or some other—is valid within acceptable limits. The third and most general situation is the one in which the family of simultaneous differential rate equations for a complex, multistep reaction... 

Samples must be representative of the environment in relation to study objectives and to permit comparison of data with appropriate standards, i.e. average concentrations, time-weighted exposures, peak concentrations, etc. Replicate samples may be advisable. 

Traditionally, the ideal extended-release product has been conceived as providing essentially stable blood levels over the whole dosing frequency interval. Thus, unlike the saw-edge blood concentration time profile of a non-controlled-release product that may show rather wild fluctuations between sub- and su-pratherapeutic blood levels, the ideal extended-release product avoids both nontherapeutic blood levels and those likely to have an increased frequency of dose-related side effects. However, in recent years con-trolled-release products that deliberately exploit a pulsatile drug release time profile have also attracted attention. 

To predict oral plasma concentration-time profiles, the rate of drug absorption (Eq. (53)) needs to be related to intravenous kinetics. For example, in the case of the one-compartment model with first-order elimination, the rate of plasma concentration change is estimated as... 

Cone JW, Gelder AH, Visscher GJW, Oudshoom L. Influence of rumen fluid and substrate concentration on fermentation kinetics measured with fully automated time related gas production apparatus. Animal Feed Science and Technology. 1996 61 113-128. 

The follicles are used to treat asthma and cough and to mitigate painful swollen breasts. A paste of the leave is applied to contusion. Essential oil distilled from the follicles induced apoptotic death in HepG2 human hepatoma cells in a concentration- and time-related manner, and inhibited tumor development of mice inoculated with Huh-7 human hepatoma cells (33). 

Half time relations are useful for finding specific rates from data because of the simplicity of the their formulas. To find the order, it is necessary to have half time data with several starting concentrations. 

Relating the Time-Course of Plasma Concentrations to the Time-Course of Effect A critical decision to be made after the first human study is whether the compound s speed of onset and duration of action are likely to be consistent with the desired clinical response. Speed of onset is clearly of interest for treatments which are taken intermittently for symptoms rehef, for example, acute treatments for migraine, analgesics, or antihistamines for hay fever. Duration of action phase I is particularly important when the therapeutic effect needs to be sustained continuously, such as for anticonvulsants. The first information on the probable time course of action often comes from the plasma pharmacokinetic profile. However, it has become increasingly evident that the kinetic profile alone may be misleading, with the concentration-time and the effect-time curves being substantially different. Some reasons for this, with examples, include... 

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