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Derivation of equations that describe the time course of change for a system with zero-order input and first-order elimination are presented in the articles Exponential decay and Biological half-life, and in scientific literature. [1] [7] = C t is concentration after time t
In this one-compartment model, the most common model of elimination is first order kinetics, where the elimination of the drug is directly proportional to the drug's concentration in the organism. This is often called linear pharmacokinetics , as the change in concentration over time can be expressed as a linear differential equation d C d t ...
A 1977 article compares the "classical" trapezoidal method to a number of methods that take into account the typical shape of the concentration plot, caused by first-order kinetics. [8] Notwithstanding the above knowledge, a 1994 Diabetes Care article by Mary M. Tai purports to have independently discovered the trapezoidal rule. [9]
[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].
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)
If () is the concentration of a substance at time , its time dependence is given by = where k is the reaction rate constant. Such a decay rate arises from a first-order reaction where the rate of elimination is proportional to the amount of the substance: [39]
The reaction changes from approximately first-order in substrate concentration at low concentrations to approximately zeroth order at high concentrations. At small values of the substrate concentration this approximates to a first-order dependence of the rate on the substrate concentration:
Each of these factors may vary from patient to patient (inter-individual variation), and indeed in the same patient over time (intra-individual variation). In clinical trials, inter-individual variation is a critical measurement used to assess the bioavailability differences from patient to patient in order to ensure predictable dosing.