Area under the curve (pharmacokinetics)

Absolute bioavailability refers to the bioavailability of a drug when administered via an extravascular dosage form (i.e. oral tablet, suppository, subcutaneous, etc.) compared with the bioavailability of the same drug administered intravenously (IV). This is done by comparing the AUC of the non-intravenous dosage form with the AUC for the drug administered intravenously. This fraction is normalized by multiplying by each dosage form's respective dose.[6]

${\displaystyle F_{\text{abs}}=\left({\frac {{\text{AUC}}_{\text{non-IV}}}{{\text{AUC}}_{\text{ IV}}}}\ \right)\times \left({\frac {{\text{Dose}}_{\text{ IV}}}{{\text{Dose}}_{\text{non-IV}}}}\ \right)}$

Relative bioavailability compares the bioavailability between two different dosage forms. Again, the relative AUCs are used to make this comparison and relative doses are used to normalize the calculation.

${\displaystyle F_{\text{rel}}=\left({\frac {{\text{AUC}}_{\text{dosageA}}}{{\text{AUC}}_{\text{dosageB}}}}\ \right)\times \left({\frac {{\text{Dose}}_{\text{B}}}{{\text{Dose}}_{\text{A}}}}\ \right)}$

The use of trapezoidal rule in AUC calculation was known in literature by no later than 1975, in J.G. Wagner's Fundamentals of Clinical Pharmacokinetics. 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] In Tai's response to the later letters to the editors, she explained that the rule was new to her colleagues, who relied on grid-counting.[10] Tai's paper has been discussed as a case of scholarly peer review failure.[11]

Despite the number of mathematically superior numerical integration schemes (such as those outlined in Wagner & Ayres 1977), the trapezoidal rule remains the convention for AUC calculation. Later focus on improving the accuracy of AUC calculation shifted from improving the method to improving the sampling scheme. An example is a 2019 algorithm known as OTTER: it performs a fit onto sum of exponentials curve for the input data but only uses it to suggest better sample times by finding more highly sloped periods.[12]

The area under the effect curve (AUEC) is an integral of the effect of a drug over time, estimated as a previously-established function of concentration. It was proposed to be used instead of AUC in animal-to-human dose translation, as computer simulation shows that it could cope better with half-life and dosing schedule variations than AUC. This is an example of a PK/PD model, which combines pharmacokinetics and pharmacodynamics.[13]