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The first pharmacokinetic model described in the scientific literature [2] was in fact a PBPK model. It led, however, to computations intractable at that time. The focus shifted then to simpler models, [3] for which analytical solutions could be obtained (such solutions were sums of exponential terms, which led to further simplifications.)
The models used in non-linear pharmacokinetics are largely based on Michaelis–Menten kinetics. A reaction's factors of non-linearity include the following: Multiphasic absorption: Drugs injected intravenously are removed from the plasma through two primary mechanisms: (1) Distribution to body tissues and (2) metabolism + excretion of the ...
The result is equivalent to the Michaelis–Menten kinetics of reactions catalyzed at a site on an enzyme. The rate equation is complex, and the reaction order is not clear. In experimental work, usually two extreme cases are looked for in order to prove the mechanism. In them, the rate-determining step can be: Limiting step: adsorption/desorption
Absorption is the journey of a drug travelling from the site of administration to the site of action. [ 1 ] [ 2 ] The drug travels by some route of administration ( oral , topical-dermal , etc.) in a chosen dosage form (e.g., tablets , capsules , or in solution ). [ 3 ]
The rate is first-order in one reactant (ethyl acetate), and also first-order in imidazole, which as a catalyst does not appear in the overall chemical equation. Another well-known class of second-order reactions are the S N 2 (bimolecular nucleophilic substitution) reactions, such as the reaction of n-butyl bromide with sodium iodide in acetone:
The kinetic derivation applies to gas-phase adsorption. However, it has been mistakenly applied to solutions. The multiple-adsorbate case is covered in the competitive adsorption sub-section. The model assumes adsorption and desorption as being elementary processes, where the rate of adsorption r ad and the rate of desorption r d are given by
In first-order (linear) kinetics, the plasma concentration of a drug at a given time t after single dose administration via IV bolus injection is given by; = / where: C 0 is the initial concentration (at t=0)
[A] can provide intuitive insight about the order of each of the reagents. If plots of v / [A] vs. [B] overlay for multiple experiments with different-excess, the data are consistent with a first-order dependence on [A]. The same could be said for a plot of v / [B] vs. [A]; overlay is consistent with a first-order dependence on [B].