# Area under the curve (pharmacokinetics)

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In the field of pharmacokinetics, the area under the curve (AUC) is the definite integral in a plot of drug concentration in blood plasma vs. time. In practice, the drug concentration is measured at certain discrete points in time and the trapezoidal rule is used to estimate AUC.

## Interpretation and usefulness of AUC values

The AUC (from zero to infinity) represents the total drug exposure across time. Assuming linear pharmacodynamics with elimination rate constant K, one can show that AUC is proportional to the total amount of drug absorbed by the body. The proportionality constant is 1/K.

This is useful when trying to determine whether two formulations of the same dose (for example a capsule and a tablet) release the same dose of drug to the body. Another use is in the therapeutic drug monitoring of drugs with a narrow therapeutic index. For example, gentamicin is an antibiotic that can be nephrotoxic (kidney damaging) and ototoxic (hearing damaging); measurement of gentamicin through concentrations in a patient's plasma and calculation of the AUC is used to guide the dosage of this drug.

AUC becomes useful for knowing the average concentration over a time interval, AUC/t. Also, AUC is referenced when talking about elimination. The amount eliminated by the body (mass) = clearance (volume/time) * AUC (mass*time/volume).

## AUC and bioavailability

In pharmacokinetics, bioavailability generally refers to the fraction of drug absorbed systemically, and is thus available to produce a biological effect. This is often measured by quantifying the "AUC". In order to determine the respective AUCs, the serum concentration vs. time plots are typically gathered using C-14 labeled drugs and AMS (accelerated mass spectroscopy).

Bioavailability can be measured in terms of "absolute bioavailablity" or "relative bioavailablity".

### Absolute bioavailability

Absolute bioavailablity refers to the bioavailability of drug when administered via a non-intravenous (non-IV) 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.

$F_{abs}=\left({\frac {AUC_{non-IV}}{AUC_{IV}}}\ \right)\times \left({\frac {Dose_{IV}}{Dose_{non-IV}}}\ \right)$ ### Relative bioavailability

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.

$F_{rel}=\left({\frac {AUC_{dosageA}}{AUC_{dosageB}}}\ \right)\times \left({\frac {Dose_{B}}{Dose_{A}}}\ \right)$ 